f a differentiable real valued function
lim h - > 0 of (f(x + ah) - f(x + bh))/h
where a,b real numbers
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.