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
Douglas K.
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.

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