Question
Construct an example of a functions which is strictly increasing but whose derivative vanishes at a point in the domain of definition of the function.
Solution
Let (x) = x3
It is strictly increasing in [– 2, 2] but f '(x) = 3 x2 ⇒ f '(0) = 0
i.e. f ' (x) vanishes at a point x = 0 ∊ [– 2, 2].
