Chapter 3, Problem 40RE

(a)

To determine

The average rate of change of function f in interval $\left[0,1\right]$ from the graph and choose the correct options.

The options are:

A) Greater than $f^{\prime }\left(0\right)$

B) Less than $f^{\prime }\left(0\right)$

C) Approximately equal to $f^{\prime }\left(0\right)$

The graph provided is:

(b)

To determine

The average rate of change of function f in interval $\left[0,2\right]$ from the graph and choose the correct options.

The options are:

A) Greater than $f^{\prime }\left(1\right)$

B) Less than $f^{\prime }\left(1\right)$

C) Approximately equal to $f^{\prime }\left(1\right)$

The graph provided is:

(c)

To determine

The instantaneous rate of change of function f in interval $\left[-2,0\right]$ from the graph and choose the correct options.

The options are:

A) Increasing

B) Decreasing

C) Neither increasing nor decreasing

The graph provided is:

(d)

To determine

The instantaneous rate of change of function f in interval $\left[-2,2\right]$ from the graph and choose the correct options.

The options are:

A) Increasing, then decreasing

B) Decreasing, then increasing

C) Approximately constant

The graph provided is:

(e)

To determine

The value of $f\left(x\right)$ at $x=0$ from the graph and choose the correct options.

The options are:

A) Approximately $0$ and increasing at the rate of about $1.5$ units per unit of x.

B) Approximately $0$ and decreasing at the rate of about $1.5$ units per unit of x.

C) Approximately $1.5$ and neither increasing nor decreasing.

D) Approximately $0$ and neither increasing nor decreasing.

The graph provided is: