NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The function x 5 - 5 x 4 + 5 x 3 - 1 is

Options

Amaximum at x = 3 and minimum at x = 1
Bminimum at x = 1
Cneither maximum nor minimum at x = 0
Dmaximum at x = 0

Correct answer

C. neither maximum nor minimum at x = 0

Step-by-step solution

Let, f x = x 5 - 5 x 4 + 5 x 3 - 1 ⇒ f ′ x = 5 x 4 − 20 x 3 + 15 x 2 = 0 ∴ x 2 x - 3 x - 1 = 0 or x = 3 , 1 , 0 Now, f ″ x = 20 x 3 − 60 x 2 + 30 x Put x = 3 , 1 , 0 , we get f ″ 3 > 0 , f ″ 1 < 0 , f ″ 0 = 0 Hence f x is minimum at x = 3 , maximum at x = 1 , neither maximum nor minimum at x = 0.

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