Published by:
CGP EDU Academic Team
Published on: August 12, 2026
The function f(x) = x 5 – 5x 4 + 5x 3 – 1 has-
Text Solution
Verified by ExpertsThe correct answer is:
D
f ′ (x) = 5x 4 – 20x 3 + 15x 2 f ′′ (x) = 20x
3 – 60x 2 + 30x
f ′ (x) = 0 ⇒ x 2 (x 2 – 4x + 3) = 0
⇒ x 2 (x – 1)(x – 3) = 0 ⇒ x = 0, 1, 3
f ′′ (1) < 0 & f ′′ (3) = 540 – 540 + 90 > 0
& f ′′ (0) = 0 & f ′′′ (0) ≠ 0
∴ Maximum at x = 1 and minimum at x = 3
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