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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

Sagot :

Absor201idn

Answer:

Average rate of change for the function [tex]f(x)= x^2-x-1[/tex] 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: [tex]f(x)= x^2-x-1[/tex]

The formula used to find average rate of change is:

[tex]Average\:rate\:of\:change=\frac{f(b)-f(a)}{b-a}[/tex]

We have, a = -1 and b = 1

Finding f(b) when b=1

[tex]f(x)=x^2-x-1\\f(1)=(1)^2-(1)-1\\f(1)=1-1-1\\f(1)=-1[/tex]

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

[tex]f(x)=x^2-x-1\\f(-1)=(-1)^2-(-1)-1\\f(1)=1+1-1\\f(-1)=2-1\\f(-1)=1[/tex]

Now, putting values and finding average rate of change

[tex]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[/tex]

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

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