Question 1 4 pts 1 Details Suppose that the position of a particle is given by 8 = f(t) = 56° +61 +9. (a) Find the velocity at time t. m2 v(t) = 8 (b) Find the velocity at time t = 3 seconds. m (c) Find the acceleration at time t. a(t) = m 32 (d) Find the acceleration at time t = 3 seconds. m/s^2

The firm should produce 3.5 units to maximize profit, but the maximum profit is -$300, indicating the firm is operating at a loss.

To find the units of production that maximize profit, we need to first find the profit function by subtracting the cost function from the revenue function:

Profit = Revenue - Cost = R - C = 1400x - (700 + 1200x) = 200x - 700

Now, to find the units of production that maximize profit, we need to find the value of x that maximizes the profit function. We can do this by taking the derivative of the profit function with respect to x and setting it equal to zero:

d(Profit)/dx = 200 - 0 = 0

Solving for x, we get:

x = 3.5

Therefore, the firm should produce 3.5 units to maximize its profit.

To find the maximum profit, we can substitute the value of x back into the profit function:

Profit = 200x - 700 = 200(3.5) - 700 = -300

So the maximum profit is -$300, which means the firm is operating at a loss. This suggests that the firm should re-evaluate its production costs and revenue strategies to try and reduce costs or increase revenue in order to achieve a positive profit.

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Answer:

i think the answer is 20.25

Step-by-step explanation:

Jayden's starting salary is $41000 per year. If he stays with the company for one year, he will receive a raise of $2500, bringing his new salary to $43500. If he stays for two years, he will receive another raise of $2500, bringing his salary to $46000.

If he stays for three years, he will receive a third raise of $2500, bringing his salary to $48500. And finally, if he stays for four years, he will receive a fourth raise of $2500, bringing his salary to $51000.

Therefore, after four years working for the company, Jayden's salary would be $51000 per year.

After t years, Jayden's salary would be calculated as follows:

- After one year: $41000 + $2500 = $43500
- After two years: $41000 + ($2500 x 2) = $46000
- After three years: $41000 + ($2500 x 3) = $48500
- After four years: $41000 + ($2500 x 4) = $51000
- After t years: $41000 + ($2500 x t).

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Using the exponential function to estimate the average price of a gallon of orange juice in 2020, the average price in 2020 is $6.39

To estimate the average price of a gallon of orange juice in 2020 using the given exponential function f(x) = 1.07(1.03^x) + 3.79, first, determine the number of years after 1990, which is r:

r = 2020 - 1990 = 30

Next, substitute r with 30 into the function:

f(30) = 1.07(1.03^30) + 3.79

Calculate the value of f(30):

f(30) ≈ 1.07(2.427) + 3.79 ≈ 2.599 + 3.79 ≈ 6.389

Round your answer to the nearest cent:

Average price in 2020 ≈ $6.39

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Answer:

The perimeter of rectangle ABCD can be calculated by adding up the lengths of its sides. Using the distance formula, we can find that AB has a length of 2 units, BC has a length of 2 units, CD has a length of 2 units, and AD has a length of 4 units. Therefore, the perimeter of rectangle ABCD is 10 units.

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If the probability of picking out a basketball card is 2/5, and the probability of picking out a football card is 1/3, the probability of Justice randomly picking out a soccer card is 4/15.

To find the probability of Justice picking out a soccer card, we need to know the total probability of all three types of cards adding up to 1. Since there are only three types of cards, we can subtract the probability of picking a basketball card and the probability of picking a football card from 1 to find the probability of picking a soccer card.

Let P(S) be the probability of picking a soccer card.

We know that P(B) = 2/5 and P(F) = 1/3.

Therefore, the total probability of picking one of the three cards is:

P(B) + P(F) + P(S) = 1

Substituting the values we know, we get:

2/5 + 1/3 + P(S) = 1

Simplifying the equation, we get:

6/15 + 5/15 + P(S) = 1

11/15 + P(S) = 1

P(S) = 1 - 11/15

P(S) = 4/15

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The solution to the given equation which is log₃(1/9) = 2x - 1 is equal to x = -1/2.

To solve the equation log₃(1/9) = 2x - 1, we need to isolate the variable x on one side of the equation. We can start by using the logarithm property that states that the logarithm of a number to a base is equal to the exponent to which the base must be raised to obtain that number. In other words, log₃(1/9) = x if and only if [tex]3^x[/tex] = 1/9.

So, let's rewrite the given equation using this property as follows:

[tex]3^{(log(1/9))[/tex] = [tex]3^{2x-1[/tex]

Simplifying the left-hand side using the logarithm property, we get:

1/9 = [tex]3^{(2x - 1)[/tex]

Now, we can solve for x by taking the logarithm of both sides to base 3:

log₃(1/9) = log₃([tex]3^{(2x - 1)[/tex])

-2 = (2x - 1) * log₃(3)

-2 = 2x - 1

2x = -1

x = -1/2

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To find the number when 28 is the geometric mean of 13 and that number, we'll use the formula for the geometric mean: √(a * b) = GM, where a and b are the two numbers, and GM is the geometric mean. In this case, a = 13, GM = 28.

Step 1: Substitute the given values into the formula:
√(13 * b) = 28

Step 2: Square both sides to get rid of the square root:
(√(13 * b))^2 = 28^2
13 * b = 784

Step 3: Divide both sides by 13 to isolate b:
b = 784 / 13
b ≈ 60.31

So, the other number is approximately 60.31 when rounded to the nearest hundredth. In summary, 28 is the geometric mean of 13 and 60.31, as √(13 * 60.31) ≈ 28.

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Answer:

1. First simplify the left-hand side of the equation using the trigonometric                      identity

sin(2t)cos(t) - cos(2t)sin(t) = sin(2t - t) = sin(t)

2. That way the equation becomes sin(t) = 0.

3. The solutions to this equation are t = kπ for all integers k.

4. Therefore, the general solution to the original equation is:

                   t = kπ or t = π/2 + kπ, where k is an integer.

Kirk would have paid $13,900 more for damages than what he had invested in his insurance policy if he did not have automobile insurance.

The amount that Kirk would have paid for damages than what he had invested in his insurance policy if he did not have automobile insurance can be determine as follows. Hence,

1. Calculate the total amount Kirk paid in insurance premiums over 8 years:

$1,075 * 8 = $8,600

2. Determine the total value of the car that was totaled:

$22,500

3. Subtract the total amount Kirk paid in insurance premiums from the value of the totaled car:

$22,500 - $8,600 = $13,900

Kirk would have paid $13,900 more for damages.

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The antiderivative of the given integral is (X^2/2) + 50X + C, where C is the constant of integration.

This is obtained by integrating the given polynomial directly without the need for trigonometric substitution.First, let's rewrite the integral: ∫(X + 34 + 16) dx. Since the integrand is a polynomial, we don't need trigonometric substitution. Instead, we can find the antiderivative directly:

∫(X + 34 + 16) dx = ∫(X + 50) dx.

Now, find the antiderivative:

(X^2/2) + 50X + C, where C is the constant of integration.

So, the antiderivative of ∫(X + 34 + 16) dx is (X^2/2) + 50X + C.

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Answer:

Step-by-step explanation:

You're going to want to break up the shape into three parts, two triangles, and the rectangle.

Starting with the left-most triangle: A=(L*W)/2

The length is 4ft and the width is 3ft, multiply and divide by 2 to get:  A=6 square feet.

Do the same with the second triangle on the bottom left (L=2ft, W=2ft) to get A=2 square feet.

Now the rectangle, A=L*W and total length is 10ft (8ft+2ft) and the width is 3ft. Multiply these values to get A=30 square feet.

Last step: add up all three areas for the total area of the entire shape, 6+2+30=38.

Area= 38 square feet.

a. The function that would best model the population over time is Exponential decay

b. write an equation that models the changing population over time  P(t) = [tex]72,000 * e^(-0.035t)[/tex]

a. Exponential rot (Exponential decay) work would best demonstrate the populace over time.

Usually, the populace has diminished from 72,000 to 70,379 in fair 2 years, which could be a generally brief time period. Also, city authorities anticipate the populace to level off at 60,000, which is a sign of exponential rot.

b. The exponential rot work can be composed as:

P(t) = P0 *[tex]e^(-kt)[/tex]

Where P(t) is the populace at time t, P0 is the starting populace, e is the scientific steady around rise to 2.718, and k is the rot consistent.

Utilizing the given data, able to substitute the values:

P(0) = 72,000 (populace in 2018)

P(2) = 70,379 (populace in 2020)

To illuminate for k, able to utilize the equation:

k = ln(P0/P(t))/t

k = ln(72,000/70,379)/2

k ≈ 0.035

Subsequently, the condition that models the changing populace over time is:

P(t) = [tex]72,000 * e^(-0.035t)[/tex]

where t is the time in a long time since 2018. 

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The product of (8-6b)(5-3b), using the distributive property of multiplication is [tex]18b^2 - 54b + 40[/tex].

This problem is actually an algebraic expression involving variables and constants. To find the product of (8-6b)(5-3b), we need to use the distributive property of multiplication.

We can start by multiplying 8 by 5, which gives us 40. Next, we multiply 8 by -3b, which gives us -24b. Then, we multiply -6b by 5, which gives us -30b. Finally, we multiply -6b by -3b, which gives us[tex]18b^2[/tex].

Putting all of these terms together, we get:
(8-6b)(5-3b) = [tex]40 - 24b - 30b + 18b^2[/tex]

Simplifying this expression, we can combine the like terms -24b and -30b to get -54b. So the final answer is:
(8-6b)(5-3b) = [tex]18b^2 - 54b + 40[/tex]

Therefore, the product of (8-6b)(5-3b) is  [tex]18b^2 - 54b + 40[/tex].

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The probability of the event not happening is 5/83.

Here, probability refers to the likelihood of a given event occurring and that the inequality f(x) > 3g(x) holds for all x > 0.

If the probability of an event happening is 88/83, then the probability of the event not happening is 1 minus the probability of the event happening. This can be expressed as:

1 - 88/83

To simplify this expression, we can first find a common denominator for 1 and 88/83, which is 83/83:

83/83 - 88/83

-5/83

Therefore, the probability of the event not happening is 5/83.

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The area of the shaded region is (9/500)π.

To find the area shaded below in circle K, we first need to find the radius of the circle.

Let O be the center of the circle, and let N be the midpoint of segment LM. We can draw a radius ON to segment LM such that it is perpendicular to LM, and then draw another radius OL to point L. This forms a right triangle LON with the hypotenuse equal to the radius of circle K.

Since segment LM is given to have a length of 11/9π, we can find the length of LN by dividing it in half:

LN = (11/9π)/2 = 11/18π

We can then use trigonometry to find the length of OL:

sin(55°) = OL / LN

OL = LN sin(55°)

OL = (11/18π) sin(55°)

Next, we can use the Pythagorean theorem to find the length of ON:

ON² = OL² + LN²

ON² = [(11/18π) sin(55°)]² + [11/18π]²

ON ≈ 1.022

Therefore, the radius of circle K is approximately 1.022.

The area of the shaded region can now be found by subtracting the area of sector LOM from the area of triangle LON:

Area of sector LOM = (110/360)π(1.022)² ≈ 0.317π

Area of triangle LON = (1/2)(11/18π)(1.022) ≈ 0.326π

Area of shaded region = (0.326π) - (0.317π) = (9/500)π

So the area of the shaded region is (9/500)π.

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An equation that best fits the data is: C. g = -0.019r² + 0.797r + 1.94.

In this scenario, the r (inches) would be plotted on the x-axis (x-coordinate) of the scatter plot while the G (inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the r (inches) and the G (inches), an equation for the line of best fit is given by:

g = -0.019r² + 0.797r + 1.94

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: We can use the formula Distance = Average speed x time to verify whether Dr Seroto left his office at exactly 10:50.

Let t be the time Dr Seroto left his office. Then, the time he arrived at the school can be expressed as:

t + (Distance/Average speed) = 11:20

We know that the distance is 45 km and the average speed is 100 km/hour. Substituting these values, we get:

t + (45/100) = 11:20

We need to convert the time on the right-hand side to hours. 11:20 can be written as:

11 + 20/60 = 11.33 hours

Substituting this value, we get:

t + 0.45 = 11.33

Solving for t, we get:

t = 11.33 - 0.45

t = 10.88 hours

This is not equal to 10:50, which is 10.83 hours. Therefore, Dr Seroto did not leave his office at exactly 10:50.

The value of T is 428°C.

To solve the problem, we can start by substituting the given value of R = 13946 into the equation R = 10000 + (4124 x 10^-2)T – (1779 x 10^-5)T^2 and solving for T. This gives us a quadratic equation in T which can be solved using the quadratic formula.

After simplifying, we get T = 427.67°C or T = -88.22°C. However, we know that the thermometer is only used if T ≤ 600°C, so the only valid solution is T = 427.67°C.Therefore, the temperature corresponding to a resistance of 13946 ohms is approximately 428°C.

It's important to note that this assumes the thermometer is operating within its specified range and that the resistance-temperature relationship remains linear over the given temperature range.

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(a) Miguel had the greatest spread in training times.

(b) Adam had the least spread in the middle 50% of training times.

(c) Miguel's training times had a greater range, indicating more variability, while Adam's training times were more consistent and tightly grouped.

(a) To determine which person had the greatest spread, we need to compare the range or variability of their training times. By observing the given data, we can see that Adam's training times range from 92 to 106, resulting in a spread of 14. On the other hand, Miguel's training times range from 85 to 105, resulting in a spread of 20. Therefore, Miguel had the greatest spread of training times.

(b) To determine which person had the least spread in the middle 50% of training times, we need to compare the interquartile range (IQR). By calculating the IQR, we find that Adam's IQR is 9 (from the 25th to the 75th percentile), whereas Miguel's IQR is 7. Since Adam's IQR is greater, it means Miguel had the least spread in the middle 50% of training times.

(c) The answers to parts (a) and (b) indicate that while Miguel had a greater spread of training times overall, Adam's training times had a greater spread in the middle 50%. This suggests that Adam's training times were more concentrated around the median, while Miguel's training times were more spread out.

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a) All of the training times of Adam had the greatest spread.

(b) The middle 50% of the training times of Adam had the least spread.

(c) The answers to Parts (a) and (b) tell us that Adam's training performance may be more stable within that middle 50%, while Miguel's performance is more variable.

(a) Adam's training times had the greatest spread.

To determine this, we can calculate the range of the data sets. For Adam, the range is 106-92 = 14 seconds, while for Miguel, the range is 105-85 = 20 seconds. However, a better measure of spread is the interquartile range (IQR), which focuses on the middle 50% of the data. For Adam, the IQR is 101-97 = 4 seconds, while for Miguel, the IQR is 96-89 = 7 seconds. In both cases, Miguel's data has a greater spread.

(b) Adam's training times had the least spread for the middle 50% of the data. This is demonstrated by the IQR, as mentioned above. For Adam, the IQR is 4 seconds, while for Miguel, it is 7 seconds.

(c) The answers to Parts 2(a) and 2(b) tell us that while Miguel's overall training times have a greater spread, the middle 50% of Adam's training times are more consistent, with less variation. This suggests that Adam's training performance may be more stable within that middle 50%, while Miguel's performance is more variable.

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the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters. So the dimensions of the rectangle are 10 meters by 11 meters.

what is  rectangle ?

A rectangle is a geometric shape that has four straight sides and four right angles (90-degree angles) between them. The opposite sides of a rectangle are parallel and have the same length, so the shape is symmetrical along its horizontal and vertical axes.

In the given question,

Let's assume that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is x + 1 meters, since the length and width are consecutive integers.

The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 42 meters, so we can write:

2(length + width) = 42

Substituting the expressions for the length and width in terms of x, we get:

2(x + x + 1) = 42

Simplifying this equation, we get:

4x + 2 = 42

Subtracting 2 from both sides, we get:

4x = 40

Dividing both sides by 4, we get:

x = 10

Therefore, the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters.

So the dimensions of the rectangle are 10 meters by 11 meters.

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To find the value of x when (fog)(x) = -8, we first need to find the composition of f and g, which is given by (fog)(x) = f(g(x)). To do this, we substitute g(x) into the expression for f(x) and simplify:

f(g(x)) = f(1) when g(x) = 1

f(g(x)) = f(-2) when g(x) = -2

f(g(x)) = f(3) when g(x) = 3

f(g(x)) = f(-4) when g(x) = -4

f(g(x)) = f(4) when g(x) = 4

There is no value of x for which (fog)(x) = -8.

Using the table given in the question, we can find the values of f(g(x)) for each possible value of g(x):

f(g(x)) = f(1) = -2

f(g(x)) = f(-2) = 0

f(g(x)) = f(3) = 32

f(g(x)) = f(-4) = 8

f(g(x)) = f(4) = 4

Therefore, (fog)(x) = -8 is not possible. The closest value we can get to -8 is by setting g(x) = -4, which gives f(g(x)) = f(-4) = 8. Thus, there is no value of x for which (fog)(x) = -8.

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The expected number of tosses until two players get different results when simultaneously tossing a coin each with a chance of heads p is (1-2p)/(2p-2p²).

The probability that both players get the same result (either both heads or both tails) on any given toss is p² + (1-p)² = 2p² - 2p + 1. The probability that they get different results (one head and one tail) is therefore 1 - (2p² - 2p + 1) = 2p - 2p².

Let E be the expected number of tosses until they end up with different results. If they get different results on the first toss, the game ends after 1 toss.

Otherwise, they have to repeat the process again, and the expected number of tosses is increased by 1. Therefore, we can express E in terms of the probabilities of getting different or same results on the first toss

E = (2p - 2p²)1 + (1 - 2p + 2p²)(1 + E)

Simplifying, we get

E = 1 + 2pE - 2p + 2p²

Rearranging and solving for E, we get

E = (1 - 2p) / (2p - 2p²)

Therefore, the expected number of tosses before the players end up with different results is (1 - 2p) / (2p - 2p²).

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Answer:

9

Step-by-step explanation:

First, let's move the variables to one side and the numbers to the other side:

[tex]\frac{2}{3}b+5=20-b\\[/tex]

subtract 5 from both sides:

[tex]\frac{2}{3}b=15-b\\[/tex]

add b to both sides:

[tex]\\1\frac{2}{3}b=15\\[/tex]

divide both sides by [tex]1\frac{2}{3}[/tex]:

[tex]b=9[/tex]

Hope this helps :)

Answer:

one

Step-by-step explanation:

The equation 4p + 7 = 3(4p) can be simplified by distributing the 3 on the right-hand side of the equation:

4p + 7 = 12p

Subtracting 4p from both sides of the equation, we get:

7 = 8p

Dividing both sides of the equation by 8, we get:

p = 7/8

Therefore, the equation has only one solution, which is p = 7/8. Answer: one.

The finance charge on a credit card account with a balance of $660.30 and an APR of 6.2% is $3.41.

To calculate the finance charge on a credit card account with a balance of $660.30 and an APR of 6.2%. Here's a step-by-step explanation:

1. Convert the APR (Annual Percentage Rate) to a decimal by dividing it by 100: 6.2 / 100 = 0.062

2. Divide the APR decimal by 12 to find the monthly interest rate: 0.062 / 12 = 0.005167

3. Multiply the credit card balance by the monthly interest rate: $660.30 * 0.005167 = $3.41

The finance charge on a credit card account with a balance of $660.30 and an Annual Percentage Rate (APR) of 6.2% is determined to be $3.41. This finance charge represents the cost of borrowing on the credit card and is calculated based on the outstanding balance and the interest rate.

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Answer:

Sure. Here are the steps on how to solve for x^3 - 1/x^3:

1. **Cube both sides of the equation x - 1/x = 3.** This will give us the equation x^3 - 3x + 1/x^3 = 27.

2. **Subtract 1 from both sides of the equation.** This will give us the equation x^3 - 1/x^3 = 26.

3. **The answer is 26.**

Here is the solution in detail:

1. **Cube both sides of the equation x - 1/x = 3.**

```

(x - 1/x)^3 = 3^3

```

```

x^3 - 3x + 1/x^3 = 27

```

2. **Subtract 1 from both sides of the equation.**

```

x^3 - 1/x^3 - 1 = 27 - 1

```

```

x^3 - 1/x^3 = 26

```

3. The answer is 26.

la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

La probabilidad de que anote un tiro libre es del 73%, lo que significa que la probabilidad de que falle es del 27%.

La probabilidad de que anote sus próximos 9 tiros libres es:

0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 x 0.73 = 0.0733

Por lo tanto, la probabilidad de que Antawn Jamison anote sus siguientes 9 tiros libres es del 7.33%.

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The combinations of side lengths that would NOT form a triangle with vertices X, Y, and Z is 7 mm , YZ = 14 mm , XZ = 25 mm.

option A.

The lengths of triangle are determined base a given set of rules;

let a, b, and c be the side lengths of a triangle;

Based on the rules of side lengths of triangles, the sum of length a and b must be greater than c, or the sum of a and c must be greater than b or the sum of b and c must be greater than a.

For option A;

7 mm + 14 mm < 25 mm (this cannot be)

For option B;

11 mm + 18 mm > 21 mm (this will work)

For option C;

11 mm + 14 mm > 21 mm (this will work)

For option D;

7 mm + 14 mm > 17 mm (this will work)

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The critical point(s) of the function f(x) = x^3 + x - 3 + 2 are determined to find the x-coordinate(s) of the local minimum or local maximum.

To find the critical point(s) of the given function, we need to first find the derivative of the function and then solve for the value(s) of x that make the derivative equal to zero.

Given function: f(x) = x^3 + x - 3 + 2

Find the derivative of the function f(x) with respect to x.

f'(x) = 3x^2 + 1

Set the derivative f'(x) equal to zero and solve for x.

3x^2 + 1 = 0

Subtract 1 from both sides of the equation.

3x^2 = -1

Divide both sides of the equation by 3.

x^2 = -1/3

Take the square root of both sides of the equation.

x = ±√(-1/3)

Since the square root of a negative number is not a real number, the function f(x) does not have any real critical points. Therefore, the critical point(s) for the function f(x) = x^3 + x - 3 + 2 is DNE (Does Not Exist) in terms of real numbers.

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