Question 1

Given the graph of $$g(x)$$ with points of inflection at $$x = -1$$ and $$x = 1$$, on which interval is the graph of $$g$$ both increasing and concave up?

Accepted Answer

$$1 \u003c x \u003c 4$$

Question 2

For the same graph, on which interval is the graph of $$g$$ both decreasing and concave up?

Accepted Answer

$$-1 \u003c x \u003c 1$$

Question 3

Which of the following best describes the behavior of $$g(x) at$$ $$x = -1$$?

Accepted Answer

Point of inflection where concavity changes from down to up

Question 4

If $$g(x) is $$concave up on an interval, which of the following must be true about $$g''(x) on $$that interval?

Accepted Answer

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

Question 5

Suppose $$g(x) is $$decreasing and concave up on $$(-1, 1). $$What does this imply about the first and second derivatives of $$g(x) on $$this interval?

Accepted Answer

$$g'(x)  0$$

Question 6

Which interval contains a local minimum of $$g(x)$$ based on the graph?

Accepted Answer

$$x \approx -3$$

Question 7

If $$g(x) is $$increasing and concave down on an interval, which of the following is true?

Accepted Answer

$$g'(x) \u003e 0$$ and $$g''(x) \u003c 0$$

Question 8

At which $$x-$$values does the graph of $$g(x)$$ change concavity?

Accepted Answer

$$x = -1$$ and $$x = 1$$

Question 9

If a particle moves along a path described by $$g(x)$$, on which interval is the particle slowing down and the path is curving upwards?

Accepted Answer

$$-1 \u003c x \u003c 1$$

Question 10

Which of the following statements is true about the graph of $$g(x) on $$the interval $$1 \u003c x \u003c 4$$?

Accepted Answer

The graph is increasing and concave up

Analyzing Graphs: Increasing/Decreasing Intervals and Concavity

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