what is the average rate of change of F(x)= x^2 +4x?

Question

given f(x)= x^2 +4x , find average rate of change of f(x) on the interval [-4, -4+h]

Answer 1

Average rate of change of a function f(x) on the interval [a,b] can be expressed as

[f(b)-f(a)]/(b-a)

f(-4) = (-4)^2+4(-4) = 0

f(-4+h) = (-4+h)²+4(-4+h) = -4h + h²

(-4h+h²)/(-4+h-(-4))=-4+h

The average rate of change of f(x) [-4,-4+h] is -4 + h