Math CentralQuandaries & Queries


Question from Brandon, a student:

i'm trying to figure out how to use the difference quotient with x^3, i have tried the following...(x+h)^2*(x+h)-(x+h)/h and i have only gotten as far as...(x^2+2xh+h^2)-(x+h)/h....i cannot see where i am goin astray, i know i am overlooking something simple, what am i overlooking?

Hi Brandon,

The difference quotient is

difference quotient

and you have f(x) = x3 so for this function the difference quotient is

difference quotient.

You can now expand (x + h)3 as (x + h)2(x + h) and then simplify the numerator but I suggest that you factor (x + h)3 - x3 as a difference of cubes.


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