Question

If a function is continuous along the interval [1,3], would it be differentiable at x=1 and x=3?

Answer 1

Not necessarily.

Explanation:

The function `f(x) = abs(x^2-4x+3)` is continuous everywhere, including `[1,3]`, but is not differentiable at `1` or at `3`.

graph{abs(x^2-4x+3) [-1.183, 6.613, -2.197, 1.7]}