How to solve for the derivative given this information: f(x+h)-f(x) = 2 h x^2 + 3 h x - 8 h^2 x + 8 h^2 - 4 h^3 ?

1 Answer
Nov 10, 2017

Given: f(x+h)-f(x) = 2 h x^2 + 3 h x - 8 h^2 x + 8 h^2 - 4 h^3

Divide both sides of the equation by h:

(f(x+h)-f(x))/h = 2x^2 + 3x - 8 h x + 8 h - 4 h^2

Compute the limit as h to 0

lim_(h to 0) (f(x+h)-f(x))/h = 2x^2 + 3x

This is the definition of the derivative.