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

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

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=(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=(f(b)-f(a))/(b-a)\\Average\:rate\:of\:change=(f(1)-f(-1))/(1-(-1))\\Average\:rate\:of\:change=(-1-(1))/(1-(-1))\\Average\:rate\:of\:change=(-1-1)/(1+1)\\Average\:rate\:of\:change=(-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