Question

Define differentiability of a function at a point.

 

Answer 1

Let  

\[f(x)\]  be a real valued function defined on an open interval 

\[(a, b)\]  and let  

\[c \in (a, b)\]

Then  

\[f(x)\]  is said to be differentiable or derivable at 

\[x = c\]

\[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\] exists finitely.

\[f'(c) = \lim_{x \to c} \frac{f(x) - f(c)}{x - c} .\]