[tex]f(x) = x^4 - 2x^3[/tex]
the average rate of change from x = −1 to x = 1
When x= -1 , f(-1)= 3
When x= 1, f(1)= -1
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
a=-1 , b= 1
Average rate of change = [tex]\frac{f(1)-f(-1)}{1-(-1)}[/tex]
Plug in the values of f(-1) and f(1)
= [tex]\frac{-1-3}{1-(-1)}[/tex]
= [tex]\frac{-4}{2} = -2[/tex]
Average rate of change = -2
Answer:
The average rate of change is [tex]-2[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=x^4-2x^3[/tex]
The average rate of change of [tex]f(x)=x^4-2x^3[/tex]
from [tex]x=-1[/tex] to [tex]x=1[/tex] is the slope of the secant line joining the points.
[tex](-1,f(-1))[/tex] and [tex](1,f(1))[/tex]
From the table,
[tex]f(-1)=3[/tex] and [tex]f(1)=-1[/tex].
Average Rate of Change
[tex]=\frac{f(1)-f(-1)}{1--1}[/tex]
[tex]=\frac{-1-3}{1--1}[/tex]
[tex]=\frac{-4}{2}[/tex]
[tex]=-2[/tex]
