Chapter 4.3, Problem 3E

(a)

To determine

To find:The way the function is increasing or increasing.

Explanation of Solution

First find the derivative of $f\left(x\right)$ that is denoted by $f^{\prime }\left(x\right)$ .

If $f^{\prime }\left(x\right)>0$ , then the graph of $f\left(x\right)$ is increasing.

If $f^{\prime }\left(x\right)<0$ , then the graph of $f\left(x\right)$ is decreasing.

Therefore, the way to define whether the function is increasing or decreasing is stated above.

(b)

To determine

To find :The way the graph of function is concave upward or downward.

Explanation of Solution

First find the derivative of $f\left(x\right)$ that is denoted by $f^{\prime }\left(x\right)$ , then the solve for second derivate $f^{″}\left(x\right)$ .

If $f^{″}\left(x\right)>0$ , then the graph of $f\left(x\right)$ is concave upward.

If $f^{″}\left(x\right)<0$ , then the graph of $f\left(x\right)$ is concave downward.

Therefore, the way to define whether the function is concave upward or downward is stated above.

(c)

To determine

To find :The way to define the point of inflection.

Explanation of Solution

First find the derivative of $f\left(x\right)$ that is denoted by $f^{\prime }\left(x\right)$ , then the solve for second derivate $f^{″}\left(x\right)$ .

Then find the points where $f^{″}\left(x\right)$ changes its sign.

Therefore, the way to define the point of inflection is stated above.