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## Homework Statement

f a differentiable real valued function

lim h - > 0 of (f(x + ah) - f(x + bh))/h

where a,b real numbers

## Homework Equations

definition of derivative

lim h-> 0 of (f(x+h) - f(x))/h

## The Attempt at a Solution

I've picked several functions like x^2 and 1/2x

in the first case you get 2xa - 2xb = 2x(a-b)

in the latter you get 1/2a - 1/2b = 1/2(a-b)

This leads me to suspect f'(x)*(a - b) as the solution, I just have no idea what to do to the limit.

I tried working backwards from my solution, but I still am missing something. Any help is appreciated.