Trying to find the right answer to this..

Let (x) = x 3 It is strictly increasing in [– 2, 2] but f '(x) = 3 x 2 ⇒ f '(0) = 0 i.e. f ' (x) vanishes at a point x = 0 ∊ [– 2, 2].

Application of Derivatives

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.

Answer

Let (x) = x³It 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].

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