Question

Calculate the average rate of change for the function f(x) = x4 + 3x3 − 5x2 + 2x − 2, from x = −1 to x = 1.

Answer 1

Answer:

The rate is change is 5.

Step-by-step explanation:

Given : $f(x) = x^4 + 3x^3 -5x^2 + 2x-2$

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,

$r=\frac{f(b)-f(a)}{b-a}$

Here, $f(x) = x^4 + 3x^3 -5x^2 + 2x-2$ and a=-, b=1

$f(1) = 1^4 + 3(1)^3 -5(1)^2 + 2(1)-2$

$f(1) =1+3-5+ 2-2$

$f(1) =-1$

$f(-1) = (-1)^4 + 3(-1)^3 -5(-1)^2 + 2(-1)-2$

$f(-1) =1-3-5-2-2$

$f(-1) =-11$

Substitute in the formula,

$r=\frac{-1-(-11)}{1-(-1)}$

$r=\frac{10}{2}$

$r=5$

Therefore, the rate is change is 5.

Answer 2

Calculate the average rate of change for the function f(x) = x4 + 3x3 − 5x2 + 2x − 2, from x = −1 to x = 1.