Question

What is the difference between continuous and differentiable?

Answer 1

The difference between continuous and differentiable functions:

Continuous function	Differentiable function
A function $f\left(x\right)$ is said to be continuous at a point $x=a$ if $f\left(a\right)$ is defined. $\underset{x\to a}{\lim }f\left(x\right)$ exists. $\underset{x\to a}{\lim }f\left(x\right)=f\left(a\right)$	A differentiable function is a function whose derivative exists at each point in its domain.
A continuous function need not be a differentiable function.	A differentiable function is also a continuous function