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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

User Yos
by
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1 Answer

9 votes

Answer:

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

User Bob Harner
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