Question 1

Given the graph of $$f(x) in $$Image 1, on which interval is the function $$f(x)$$ constant?

Accepted Answer

$$(-2, 3)$$

Question 2

For the function $$f(x)$$ shown in Image 1, at which $$x-$$value does $$f(x)$$ attain a local maximum?

Accepted Answer

$$x = 6$$

Question 3

Based on the graph of $$f(x) in $$Image 1, which interval is $$f(x)$$ decreasing?

Accepted Answer

$$(-5, -2)$$

Question 4

Given the graph of $$f'(x) in $$Image 2, on which interval is $$f(x)$$ concave downward?

Accepted Answer

$$(-2, 2)$$

Question 5

According to the table in Image 3, if $$f''(x) \u003c 0$$ and $$f'(x) is $$decreasing, what can you conclude about the graph of $$f(x)$$?

Accepted Answer

It is concave downward.

Question 6

Suppose $$f'(c) = 0$$ and $$f''(c) \u003e 0. $$According to the table in Image 5, what does this indicate about $$f(x) at$$ $$x = c$$?

Accepted Answer

$$f(x)$$ has a local minimum at $$x = c.$$

Question 7

If $$f'(x) is $$positive and $$f''(x) is $$negative on an interval, what can you say about $$f(x) on $$that interval?

Accepted Answer

$$f(x) is $$increasing and concave downward.

Question 8

Given the graph of $$f'(x) in $$Image 2, at which $$x-$$value does $$f(x)$$ have a local maximum?

Accepted Answer

$$x = -2$$

Question 9

If $$f'(x)$$ changes from negative to positive at $$x = c$$, what does the First Derivative Test tell you about $$f(x) at$$ $$x = c$$?

Accepted Answer

$$f(x)$$ has a local minimum at $$x = c.$$

Question 10

Suppose $$f''(x)$$ changes sign at $$x = c$$ and $$f is $$continuous at $$c. $$What is $$x = c$$ called?

Accepted Answer

An inflection point

Question 11

If $$f'(x) = 0$$ and $$f''(x) = 0 at$$ $$x = c$$, what does the Second Derivative Test indicate?

Accepted Answer

The test does not apply.

Question 12

Which of the following best describes the relationship between $$f'(x)$$ and the intervals where $$f(x) is $$increasing?

Accepted Answer

$$f(x) is $$increasing where $$f'(x) \u003e 0.$$

Question 13

If $$f''(x) \u003e 0$$ for all $$x in an $$interval, what does this tell you about the graph of $$f(x)$$?

Accepted Answer

It is concave upward on that interval.

Question 14

Given the graph of $$f(x) in $$Image 1, which interval is $$f(x)$$ increasing?

Accepted Answer

$$(-5, -3)$$ and $$(3, 6)$$

Chapter 4: Graphing and Optimization – Business Calculus Study Notes

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