Chapter 3.5, Problem 35E

Let f have the graph shown.

a. The average rate of change of f over $\left[2,4\right]$

is

(A) greater than $f^{\prime }\left(2\right)$.

(B) less than $f^{\prime }\left(2\right)$.

(C) approximately equal to $f^{\prime }\left(2\right)$.

b. The average rate of change of f over $\left[-1,1\right]$

is

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

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

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

c. Over the interval $\left[0,2\right]$ theinstantaneous rate of change of f is

(A) increasing.

(B) decreasing.

(C) neither.

d. Over the interval $\left[0,200\right]$ theinstantaneous rate of change of f is

(A) increasing, then decreasing.

(B) decreasing, then increasing.

(C) always increasing.

(D) always decreasing.

e. when $x=4,f\left(x\right)$

is

(A) approximately 0 and increasing at a rate of about 0.7 units per unit of x.

(B) approximately 0 and decreasing at a rate of about 0.7 units per unit of x.

(C) approximately 0.7 and increasing at a rate of about 1 units per unit of x.

(D) approximately 0.7 and decreasing at a rate of about 3 units per unit of x.