Question

Can you deeply explain how to do problems like this

Answer 1

Given a function f(x), to find the average rate of change over the interval:

`a\leq x\leq b`

we have the following expression:

`(f(b)-f(a))/(b-a)`

in this case, we have the following interval:

this means that a = -9 and b =-2. Now, lets find g(-9) and g(-2):

`\begin{gathered} g(-9)=(-9)^2+5(-9)+1=81-45+1=37 \\ g(-2)=(-2)^2+5(-2)+1=-5 \end{gathered}`

then, using the formula for the average rate of change for the function g(x), we get:

`(g(b)-g(a))/(b-a)=(g(-2)-g(-9))/(-2-(-9))=(-5-37)/(-2+9)=-(42)/(7)=-6`

therefore, the rate of change is -6