Answer:
2
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 ] = [ - 3, 7 ] , then
f(b) = f(7 ) = - 7² + 6(7) + 17 = - 49 + 42 + 17 = 10
f(a) = f(- 3) = - (- 3)² + 6(- 3) + 17 = - 9 - 18 + 17 = - 10
average rate of change = [tex]\frac{10-(-10)}{7-(-3)}[/tex] = [tex]\frac{10+10}{7+3}[/tex] = [tex]\frac{20}{10}[/tex] = 2
