Chapter 4.3, Problem 2E

(a)

To determine

To find:The open intervals on which $f$ is concave up ward.

Answer to Problem 2E

interval is $\left(0,2\right)$

Explanation of Solution

Consider the given graph.

The function is concave upward on $\left(0,2\right)$ .

Therefore, the required interval is $\left(0,2\right)$ .

(b)

To determine

To find :The open intervals on which $f$ is concave downward.

Answer to Problem 2E

interval is $\left(2,4\right)\text{and}\left(4,6\right)$

Explanation of Solution

Consider the given graph.

The function is concave downward on $\left(2,4\right)\text{and}\left(4,6\right)$ .

Therefore, the required interval is $\left(2,4\right)\text{and}\left(4,6\right)$ .

(c)

To determine

To find :The coordinates of the point of inflection.

Answer to Problem 2E

point is $\left(2,3\right),\left(4,1\right)$ .

Explanation of Solution

Consider the given graph.

The inflection points are the points where the graph changes from concave up to concave down or vice-verse.

The point inflections are $\left(2,3\right),\left(4,1\right)$

Therefore, the required point is $\left(2,3\right),\left(4,1\right)$ .