Answer:
The rate is change is 5.
Step-by-step explanation:
Given : [tex]f(x) = x^4 + 3x^3 -5x^2 + 2x-2[/tex]
To find : Calculate the average rate of change for the function from x = -1 to x = 1 ?
Solution :
The rate of change of function from a to b is given by,
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]
Here, [tex]f(x) = x^4 + 3x^3 -5x^2 + 2x-2[/tex] and a=-, b=1
[tex]f(1) = 1^4 + 3(1)^3 -5(1)^2 + 2(1)-2[/tex]
[tex]f(1) =1+3-5+ 2-2[/tex]
[tex]f(1) =-1[/tex]
[tex]f(-1) = (-1)^4 + 3(-1)^3 -5(-1)^2 + 2(-1)-2[/tex]
[tex]f(-1) =1-3-5-2-2[/tex]
[tex]f(-1) =-11[/tex]
Substitute in the formula,
[tex]r=\frac{-1-(-11)}{1-(-1)}[/tex]
[tex]r=\frac{10}{2}[/tex]
[tex]r=5[/tex]
Therefore, the rate is change is 5.
