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#