Science:Math Exam Resources/Courses/MATH110/December 2013/Question 10 (a)/Solution 1

A function $f(x)$ is differentiable at the point $x=2$ if the following limit exists

$\underset{x\to 2}{\lim }\frac{f(x)-f(2)}{x-2}$

Equivalently, $f(x)$ is differentiable at the point $x=2$ if the following limit exists

$\underset{h\to 0}{\lim }\frac{f(2+h)-f(2)}{h}$