Let f x be a cubic function such that f ′ 1 = f ″ 2 = 0. If x = 1 is a point of local maxima of f x , then the local minimum value of f x occurs at

Question

Let f x be a cubic function such that f ′ 1 = f ″ 2 = 0. If x = 1 is a point of local maxima of f x , then the local minimum value of f x occurs at, x = 0, x = 2, x = 4, x = 3

MARKS App · Accepted Answer

Let f ″ x = 6 λ x − 2 ⇒ f ' x = 3 λ x 2 − 4 x + c As f ′ 1 = 0 ⇒ c = 9 λ i.e. f ' x = 3 λ x 2 − 4 x + 9 λ Also, f ' 3 = 0 Hence, x = 3 is the other point of extrema.

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