Question 1

Which of the following statements about the function shown in the graph is TRUE?

Accepted Answer

The function has a relative maximum at $$x \approx -1.$$

Question 2

Based on the graph, what is the absolute maximum value of $$f(x)$$?

Accepted Answer

$$f(x) = 4$$

Question 3

Does the function shown in the graph have an absolute minimum? If so, what is it?

Accepted Answer

Yes, the absolute minimum is $$f(x) = -\infty.$$

Question 4

At which $$x-$$value does the function achieve a relative maximum?

Accepted Answer

$$x = -4$$

Question 5

Which of the following best describes the end behavior of the function as $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 6

Which of the following intervals is the function decreasing?

Accepted Answer

$$(-\infty, -1)$$ and $$(1, \infty)$$

Question 7

Suppose the function represents the height of a roller coaster over time. At which point is the roller coaster at its highest?

Accepted Answer

At $$x = -4$$

Question 8

If the function is $$f(x)$$, which of the following statements is TRUE about the critical points?

Accepted Answer

There is a relative maximum at $$x = -4$$ and a relative minimum at $$x = -1.$$

Question 9

Which of the following best describes the behavior of $$f(x) as$$ $$x 	o -\infty$$?

Accepted Answer

$$f(x)$$ approaches a finite value.

Question 10

If the graph represents the profit of a company over time, what does the relative maximum represent?

Accepted Answer

The time when profit is highest before it starts to decrease.

Calculus Exam 2 Review: Extrema, Graph Analysis, and Optimization

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