The line y = x + 1 is a tangent to the curve y 2 = 4x at the point
(1, 2)
(2, 3)
(1, -2)
(1, -2)
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.
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].