Properties of Functions & Average Rate of Change

Question

Find the average rate of change of f(x)=x³-8x+7

over the following intervals:

a: from -8 to -4

b: from -1 to 1

c: from 1 to 7

Answer 1

Average rate of change is just the slope of the secant line or the slope between the two points on the function curve like this:

So if x = -8, then f(-8) = -441 so that point is (-8, -441)

If x = -4, then f(-4) = -25 so that point is (-4, -25)

Meaning m = (-25 - -441)/(-4 - -8) = 416/4 = 104

So the average rate of change is 104

meaning that "y" or f(x) changes an average of 104 units for every 1 unit that "x" changes.

Repeat this process for the other intervals