Question

True or false?

If f is continuous at x = c, then f is differentiable at x = c.

Answer 1

not so.

consider y = |x|

Any time there's a cusp, or pointy place, on the graph, f is continuous, but since the slope changes instantly from one value to another, it is not differentiable there.

Answer 2

or, if the slope is vertical, there's no derivative there.

y = ∛x