Answer:
- 6
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 1, 4 ] , then
f(b) = f(4) = 4³ - 6(4)² - 4 = 64 - 96 - 4 = - 36
f(a) = f(- 1) = (- 1)³ - 6(- 1)² - (- 1) = - 1 - 6 + 1 = - 6 , then
average rate of change = [tex]\frac{-36-(-6)}{4-(-1)}[/tex] = [tex]\frac{-36+6}{4+1}[/tex] = [tex]\frac{-30}{5}[/tex] = - 6
