How do you find the average rate of change of $f(x)=x^2+2$ over [-2,1]?

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Answer 1 · 2015-10-13T11:32:42

$-2/3$

This is equivalent to asking for the average slope of the function between the 2 endpoints.

So we can find the function values at the 2 endpoints and then join the 2 and find the gradient of the straight line joining them.

$f(-2)=(-2)^2+2=6$
$f(1)=1^2+2=3$

Thus gradient $m=(Deltay)/(Deltax)=(3-6)/(1-(-2))=-2/3$

How do you find the average rate of change of f(x)=x^2+2f(x)=x^2+2 over [-2,1]?