# What are differentiable points for a function?

##### 1 Answer

Dec 3, 2015

A differentiable point of a function

#lim_(h->0) (f(a+h)-f(a))/h#

#### Explanation:

For example, let us verify that

Let

Then:

#lim_(h->0) (f(a+h)-f(a))/h#

#=lim_(h->0) (f(2+h)-f(2))/h#

#=lim_(h->0) (((2+h)^2+(2+h))-(2^2+2))/h#

#=lim_(h->0) ((4+4h+h^2+2+h)-(4+2))/h#

#=lim_(h->0) (5h+h^2)/h#

#=lim_(h->0) (5+h)#

#=5#