Se the table below of the function f (x) = x4 - 2x3 to answer this question:

xf (x) - 13001-120327

What is the average rate of change from x = - 1 to x = 2?

Answer: The average rate of change from x=-1 to x=2 is - 1

Solution:

f (x) = x^4-2x^3

x f (x)

-1 3

0 0

1 - 1

2 0

3 27

Average rate of change from x=-1 to x=2: r=?

Average rate of change from x=a to x=b: r=[f (b) - f (a) ] / (b-a); a=-1, b=2

a=-1→f (a) = f (-1) = 3 See table

b=2→f (b) = f (2) = 0 See table

Replacing the values in the formula:

r = (0-3) / (2 - (-1))

r = (-3) / (2+1)

r = (-3) / (3)

r=-1

Answer: The average rate of change from x=-1 to x=2 is - 1