Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The average rate of change of h(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [a, b ] = [ - 2, 2 ], thus
f(b) = f(2) = [tex]\frac{1}{8}[/tex] × 2³ - 2² = 1 - 4 = - 3
f(a) = [tex]\frac{1}{8}[/tex] × (- 2)³ - (- 2)² = - 1 - 4 = - 5
average rate of change = [tex]\frac{-3-(-5)}{2-(-2)}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
