Q.18 - Calculus

Question

Suppose f is a function whose average value on $[-3,1]$ is

$-2$ and whose average rate of change on the same in-

terval is $4$. 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 graph is 

The function is $f\left(x\right)=4x+2$

Step 1.Given data

We have to find the possible function from given constraint .

Step 2.We are drawing the possible graph for given constraints

The possible graph is 

$f\left(x\right)=4x+2$

Step 3. Writing the possible function

The graph has a slope of 4 

The rate of change of this graph is 4

The average height of given function is $-2$ in given interval $[-3,1]$