Question 1

Given the graph in the first image, which interval is $$f(x)$$ increasing?

Accepted Answer

$$(-2, 0)$$

Question 2

For the function in the first image, at which $$x-$$value does $$f(x)$$ attain a relative minimum?

Accepted Answer

$$x = 1$$

Question 3

Based on the first graph, on which interval is $$f(x)$$ concave up?

Accepted Answer

$$(0, 2)$$

Question 4

From the first image, what is the $$x-$$value of the inflection point of $$f(x)$$?

Accepted Answer

$$x = 0$$

Question 5

In the second image, which interval is $$f(x)$$ decreasing?

Accepted Answer

$$(1, 3)$$

Question 6

For the function in the second image, at which $$x-$$value does $$f(x)$$ attain a relative maximum?

Accepted Answer

$$x = 1$$

Question 7

Based on the second graph, on which interval is $$f(x)$$ concave down?

Accepted Answer

$$(1, 3)$$

Question 8

From the second image, what is the $$x-$$value of the inflection point of $$f(x)$$?

Accepted Answer

$$x = 2$$

Question 9

Suppose a business's profit function $$P(x) is $$represented by the solid curve in the first image. At which $$x-$$value should the business operate to maximize profit?

Accepted Answer

$$x = 1$$

Question 10

If the dashed curve in the second image represents the cost function $$C(x)$$, at which $$x-$$value does the cost reach its minimum?

Accepted Answer

$$x = 0$$

Question 11

Given the first image, which interval best describes where $$f(x) is $$both increasing and concave up?

Accepted Answer

$$(0, 2)$$

Question 12

In the context of the second image, if $$f(x)$$ models the revenue of a company, at which $$x-$$value does the company experience a change in the rate of revenue growth?

Accepted Answer

$$x = 2$$

Question 13

For the function in the first image, which interval is $$f(x)$$ decreasing and concave down?

Accepted Answer

$$(-3, -2)$$

Question 14

Based on the second image, which $$x-$$value is a point of inflection for the dashed curve?

Accepted Answer

$$x = 2$$

Question 15

Suppose the solid curve in the first image represents the cost function $$C(x)$$ for producing $$x$$ units. At which $$x-$$value does the cost function change from concave down to concave up?

Accepted Answer

$$x = 0$$

Question 16

In the second image, which interval is the solid curve $$f(x)$$ both increasing and concave up?

Accepted Answer

$$(-2, 1)$$

Analyzing Functions: Intervals, Extrema, and Concavity

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