Question

Given the function f(x) = x² + 3x - 2 What is the average rate of change for the function from 2 to 6? Show your work.

Answer 1

The average rate of change is 11

Explanation:

The given function is $f(x)=x^{2}+3 x-2$

We need to determine the average rate of change for the function from 2 to 6

The average rate of change can be determined using the formula,

$\frac{f(b)-f(a)}{b-a}$

where $a=2$ and $b=6$

Now, we shall determine the values of f(2) and f(6) by substituting the values for x = 2 and x = 6 in the function $f(x)=x^{2}+3 x-2$

Thus, we have,

$f(2)=2^{2}+3 (2)-2$

       $=4+6-2$

$f(2)=8$

Similarly, substituting x = 6, we get,

$f(6)=6^{2}+3 (6)-2$

       $=36+18-2$

$f(6)=52$

Hence, substituting these values in the formula $\frac{f(b)-f(a)}{b-a}$ , we get,

$\frac{f(b)-f(a)}{b-a}=\frac{52-8}{6-2}$

Simplifying, we get,

$\frac{f(b)-f(a)}{b-a}=\frac{44}{4}=11$

Thus, the average rate of change for the function from 2 to 6 is 11