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Maths Differentiation and Applications of Derivatives NTA Abhiyas Question - Applications of Derivativas Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

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

maximum at x = 3 and minimum at x = 1

minimum at x = 1

neither maximum nor minimum at x = 0

maximum at x = 0

Text Solution

Verified by Experts

The correct answer is:

neither maximum nor minimum at x = 0

Let, f(x) = x 5 -5x 4 + 5x 3 -1

f' (x) = 5x 4 – 20x 3 + 15x 2 = 0

x 2 (x - 3) (x-1) = 0 or x = 3,1, 0

Now, f" (x) = 20x 3 – 60x 2 + 30x

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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