Question

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

Answer 1

Answer:

D. 5

Step-by-step explanation:

From the information given:

The derivatives of functions and functions have a different average rate. The average rate expanded over an interval of two distinct point (a f(a)) and (b f(b)) is represented by the equation:

$\dfrac{f(b)-f(a)}{b-a}$

where; the two points are:

(-1 , f( -1) )    &    ( 1,  f(1) )

For f(1); we have:

f(1) = 1 +3(1)³ - 5(1)² + 2(1) - 2

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

f(1) = - 1

For  f( -1); we have:

(-1)⁴ + 3(-1)³ - 5(-1)²+2(-1)-2

= 1 - 3 - 5 -2 - 2

= -11

∴

$=\dfrac{-1-(-11)}{1 - (-1)}$

$=\dfrac{-1+11}{1 +1}$

$=\dfrac{10}{2}$

= 5