Question 1

Given the graph of $$y = j(x) as $$shown, at which $$x-$$value does $$j'(x)$$ most likely equal zero?

Accepted Answer

$$x = 2$$

Question 2

Which of the following best describes the behavior of $$j'(x) on $$the interval $$1 \u003c x \u003c 2$$ based on the graph of $$j(x)$$?

Accepted Answer

$$j'(x) is $$positive and decreasing

Question 3

At which $$x-$$value does the function $$j(x)$$ have a local maximum, and what does this imply about $$j'(x) at $$that point?

Accepted Answer

$$x = 2$$, and $$j'(2) = 0$$

Question 4

If the slope of $$j(x) is $$steepest and negative at $$x = 3$$, what can you say about $$j'(3)$$?

Accepted Answer

$$j'(3) is a $$large negative value

Question 5

Suppose $$j(x)$$ represents the height of a roller coaster over time. At which point is the roller coaster at its highest and momentarily at rest?

Accepted Answer

At the local maximum, where $$j'(x) = 0$$

Question 6

If $$j(x)$$ has a sharp corner at $$x = 2$$, what can you say about $$j'(2)$$?

Accepted Answer

$$j'(2)$$ does not exist

Question 7

On the interval $$4 \u003c x \u003c 6$$, the graph of $$j(x) is $$increasing. What does this indicate about $$j'(x) on $$this interval?

Accepted Answer

$$j'(x) \u003e 0$$

Question 8

If $$j(x) is $$decreasing and concave up on $$2 \u003c x \u003c 4$$, what can you say about $$j'(x)$$ and $$j''(x) on $$this interval?

Accepted Answer

$$j'(x)  0$$

Question 9

Which of the following statements is true about the derivative $$j'(x) at a $$point where $$j(x)$$ has a horizontal tangent?

Accepted Answer

$$j'(x) = 0$$

Question 10

If $$j(x)$$ has a discontinuity at $$x = 2$$, what is most likely true about $$j'(2)$$?

Accepted Answer

$$j'(2)$$ does not exist

Question 11

Suppose $$j(x)$$ models the temperature of a chemical reaction over time. If $$j'(x) is $$negative for $$2 \u003c x \u003c 4$$, what does this indicate about the reaction?

Accepted Answer

The temperature is decreasing over time

Question 12

If $$j(x) is $$constant on an interval, what is true about $$j'(x) on $$that interval?

Accepted Answer

$$j'(x) = 0$$

Analyzing and Sketching the Derivative from a Graph

Study Guide - Practice Questions

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