Question

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

xf(x)

−13 00 1−1 20 327

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

Answer 1

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