Q.17 - Calculus

Question

Suppose f is a function whose average value on

$[-2,5]$ is $10$ and whose average rate of change on

the same interval is $-3$. Sketch a possible graph for f .

Illustrate the average value and the average rate of change

on your graph of f.

Step-by-Step Solution

Answer

The average height of the graph on interval $[-2,5]$is$10$.

The rate of change is$-3$.

Step.1 Given Information

The average value of function f on the interval$[-2,5]$ is $10$and whose average rate of change is$-3$.

Step 2. Function expression.

Let the function be,

$f\left(x\right)= -3x+ 16$

The graph has a slope of -3 so, its rate of change is$-3$

The average height of the graph on the interval$[-2,5]$ is$10$.

Therefore, the function is$f\left(x\right)= -3x+ 16$.