Answer:
3
Step-by-step explanation:
The average rate of change of g(x) in the closed interval [ a, b ] is
[tex]\frac{g(b)-g(a)}{b-a}[/tex]
Here [ a, b ] = [ - 3, 2 ], thus
g(b) = g(2) = - 2² + 2(2) + 8 = - 4 + 4 + 8 = 8
g(a) = g(- 3) = - (- 3)² + 2(- 3) + 8 = - 9 - 6 + 8 = - 7
average rate of change = [tex]\frac{8-(-7)}{2-(-3)}[/tex] = [tex]\frac{15}{5}[/tex] = 3
