$$g(x)$$ approaches $$+\\infty$$

Question 1

Given the function $$g(x) = 3x^2$ - 12x + 7$$, which of the following is the $$x-$$coordinate of a critical point?

Accepted Answer

$$x = 2$$

Question 2

For the function $$f(x) = x^2$ - 8x + 6$$, use the FIRST Derivative Test to determine the nature of the critical point at $$x = 4.$$

Accepted Answer

It is a minimum.

Question 3

For $$f(x) = 5 - 2x - x^2$, use the SECOND Derivative Test to determine the nature of the critical point at x = -1$.

Accepted Answer

It is a maximum.

Question 4

Does the function $$g(x) = \frac{5x}{x+3}$$ have any vertical asymptotes? If so, where?

Accepted Answer

Yes, at $$x = -3$$

Question 5

Which of the following best describes how to find critical points for a function $$f(x)$$?

Accepted Answer

Set $$f'(x) = 0$$ and solve for $$x$$

Question 6

A business models its profit with $$P(x) = 3x^2$ - 12x + 7. $$What is the $$x-$$coordinate where profit is stationary?

Accepted Answer

$$x = 2$$

Question 7

For $$f(x) = x^2$ - 8x + 6$$, what is the sign of $$f'(x)$$ just to the left of $$x = 4$$?

Accepted Answer

Negative

Question 8

For $$f(x) = 5 - 2x - x^2$, what is the value of the second derivative f$$''(x)$$ at x = -1$?

Accepted Answer

$$-2$$

Question 9

Which of the following statements about vertical asymptotes is correct?

Accepted Answer

A vertical asymptote occurs where the denominator of a rational function is zero and the numerator is not zero.

Question 10

If $$g(x) = \frac{5x}{x+3}$$, what happens to $$g(x) as$$ $$x$$ approaches $$-3$$ from the right?

Accepted Answer

$$g(x)$$ approaches $$+\infty$$

Question 11

For $$f(x) = x^2$ - 8x + 6$$, what is the value of $$f''(x) at$$ $$x = 4$$?

Accepted Answer

$$2$$

Question 12

A company models its revenue as $$R(x) = 5 - 2x - x^2$. What does the SECOND Derivative Test indicate about the critical point at x = -1$?

Accepted Answer

The critical point is a maximum.

Question 13

Which of the following is NOT a step in applying the FIRST Derivative Test?

Accepted Answer

Check the value of $$f''(x) at $$the critical point.

Question 14

For $$g(x) = 3x^2$ - 12x + 7$$, what is the value of $$g'(x) at$$ $$x = 2$$?

Accepted Answer

$$0$$

Question 15

If a function $$f(x)$$ has a critical point at $$x = a$$ and $$f''(a) \u003c 0$$, what does this indicate?

Accepted Answer

There is a local maximum at $$x = a$$

Question 16

For $$g(x) = \frac{5x}{x+3}$$, what is the domain of the function?

Accepted Answer

All real numbers except $$x = -3$$

Question 17

A function $$f(x)$$ has a critical point at $$x = 4. If$$ $$f'(x)$$ changes from negative to positive at $$x = 4$$, what does this indicate?

Accepted Answer

There is a local minimum at $$x = 4$$

Question 18

For $$g(x) = 3x^2$ - 12x + 7$$, what is the value of the second derivative $$g''(x)$$?

Accepted Answer

$$6$$

Question 19

If $$g(x) = \frac{5x}{x+3}$$, what is the horizontal asymptote of the function?

Accepted Answer

$$y = 1$$

Business Calculus: Critical Points, Derivative Tests, and Asymptotes

Study Guide - Practice Questions