Question

Can a maximum value of a continuous function f(x) on [a,b] occur at a point c in [a,b] where f'(c) does not exist?

Answer 1

I was thinking no, because it wouldn't be continuous then? Any second opinion?

Answer 2

That would imply f(x) has an asymptote, hole, discontinuity, corner, cusp... so, what would you consider f(x) then?

Answer 3

discontinuous?

Answer 4

That is what I would think.

Answer 5

it can ocur

Answer 6

If it is a corner or cusp.

Answer 7

yeah