Question

Given the function g(x)=x^2+2x-5g(x)=x

Answer 1

We have been given a function $g(x)=x^2+2x-5$. We are asked to find average rate of change of the function over the interval $-6\leq x\leq 1$.

We will use average rate of change formula to solve our given problem.

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

For our given function $b=1$ and $a=-6$.

$\text{Average rate of change}=\frac{g(1)-g(-6)}{1-(-6)}$

$g(1)=1^2+2(1)-5$

$g(1)=1+2-5$

$g(1)=-2$

$g(-6)=(-6)^2+2(-6)-5$

$g(-6)=36-12-5$

$g(-6)=19$

$\text{Average rate of change}=\frac{-2-19}{1+6}$

$\text{Average rate of change}=\frac{-21}{7}$

$\text{Average rate of change}=-3$

Therefore, the average rate of change of the function is $-3$ over the interval $-6\leq x\leq 1$.