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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