Question

is every continuous function differentiable?

Answer 1

Determine if every continuous function is differentiable

A function is said to be continuous if its graph is continuous and does not break at any point. The graph of a continuous function can be drawn without lifting the pen off the paper.

For example, A function is said to be differentiable if it can be differentiated at every point on the curve which means that its derivative exists everywhere in the domain.

Considering a function, $f\left(x\right)=\left|x\right|$ we see that the function is continuous but not differentiable at $x=0.$

Hence, every continuous function is not differentiable.