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

1 Answer
Trevor Ryan.
Oct 13, 2015

#-2/3#

Explanation:

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#

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