Question

What is the average rate of change of f over the interval -1 on a separate sheet of paper and upload the work as a photo. Show all
appropriate work necessary for full credit.
f(x)=
x² - x - 1

Answer 1

Answer:

Average rate of change for the function $f(x)= x^2-x-1$ over the interval -1<x<1 is -1

Step-by-step explanation:

We need to find average rate of change of f over the interval -1 < x < 1

The function given is: $f(x)= x^2-x-1$

The formula used to find average rate of change is:

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

We have, a = -1 and b = 1

Finding f(b) when b=1

$f(x)=x^2-x-1\\f(1)=(1)^2-(1)-1\\f(1)=1-1-1\\f(1)=-1$

Now, finding f(a), when a= -1

$f(x)=x^2-x-1\\f(-1)=(-1)^2-(-1)-1\\f(1)=1+1-1\\f(-1)=2-1\\f(-1)=1$

Now, putting values and finding average rate of change

$Average\:rate\:of\:change=\frac{f(b)-f(a)}{b-a}\\Average\:rate\:of\:change=\frac{f(1)-f(-1)}{1-(-1)}\\Average\:rate\:of\:change=\frac{-1-(1)}{1-(-1)}\\Average\:rate\:of\:change=\frac{-1-1}{1+1}\\Average\:rate\:of\:change=\frac{-2}{2}\\Average\:rate\:of\:change=-1$

So, average rate of change for the function $f(x)= x^2-x-1$ over the interval -1<x<1 is -1