Evaluate the difference quotient for the given function. Simplify your answer. f(x) = −x3, f(a + h) − f(a)/h?

Please read :

f(x) = -x^3
[f(a + h) - f(a) / h
= -[(a + h)^3 - (-a^3) / h
= -[(a^3 + 3a^2h + 3ah^2 + h^3) + a^3]/h
= -3a^2 - 3ah - h^2

f(x) = -x^3 <----this is your variable function

f(a+h) - f(a)/h <---this is your function with substituted numbers which are represented by letters

f(a+h) = -(a+h)^3
f(a) = -(a)^3

so f(a+h) - f(a)/h = [-(a+h)^3] - [-(a)^3]/h

f(a+h) - f(a)/h = a^3/h - (a+h)^3