If a differentiable function f : (a, b) - R assumes a maximum or a minimum at some x in (a, b), prove that f'(x) = 0. Why is the assertion false

If a differentiable function f : (a, b) -> R assumes a maximum or a minimum at some x in (a, b), prove that f'(x) = 0. Why is the assertion false when [a,b] replaces (a,b)?

If a differentiable function f : (a, b) -> R assumes a maximum or a minimum at some x in (a, b),prove that f'(x) = 0. Why is the assertion false when [a,b] replaces (a,b)? Let f(x) has minimum...