Thread: Best approximation

Prove:

If is defined for and there is a number such that

where

then is differentiable at and

Originally Posted by cgiulz

Prove:

If is defined for and there is a number such that

where

then is differentiable at and

My first thought was "what is your definition of 'differentiable'?". Can we take it that this is in R and we are using the Calculus I definition of the derivative: ? If so, just put x= a+h in your formula for f(x) and put that into the difference quotient.