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 ] = [ - 5, - 1 ] , thus
f(b) = f(- 1) = - (- 1)² - 4(- 1) + 6 = - 1 + 4 + 6 = 9
f(a) = f(- 5) = - (- 5)² - 4(- 5) + 6 = - 25 + 20 + 6 = 1 , then
average rate of change = [tex]\frac{9-1}{- 1-(-5)}[/tex] = [tex]\frac{8}{4}[/tex] = 2
