Question
Compute F'(-4) where F(x) = x^3 + X^2 (using the definition of the derivative)
Answers
Steve
F'(-4)
= lim(h->0) [((-4+h)^3 + (-4+h)^2) - ((-4)^3+(-4)^2)]/h
= lim(h->0) [(h^3-11h^2+40h-48)-(-48)]/h
= lim(h->0) (h^3-11h^2+40h)/h
= lim(h->0) (h^2-11h+40)
= 40
= lim(h->0) [((-4+h)^3 + (-4+h)^2) - ((-4)^3+(-4)^2)]/h
= lim(h->0) [(h^3-11h^2+40h-48)-(-48)]/h
= lim(h->0) (h^3-11h^2+40h)/h
= lim(h->0) (h^2-11h+40)
= 40