Find positive real numbers ‘a’ and ‘b’ such that f(x) = ax …

Maths Differentiation and Applications of Derivatives General Single Correct MCQ

Published on: August 14, 2026

Find positive real numbers ‘a’ and ‘b’ such that f(x) = ax – bx 3 has four extrema on [–1 , 1] at each of which | f(x) | = 1

Text Solution

Verified by Experts

The correct answer is:

(a = 3 , b = 4 )

f’(x) = 0 ⇒ x =

f =

f(–1) = b – a

f(1) = a – b

Given that = = | b – a | = | a – b | = 1

⇒ = 1 ⇒ b = ⇒ a – b = 1 ⇒ a – = 1 ⇒ 4a 3 – 27a + 27 = 0

a = –3,

⇒ a = – 3 – 1 : b = = –

= – 4

Also , b – a = 1 ⇒ – a ⇒ 4a 3 – 27a – 27 = 0 ⇒ (a – 3) (2a + 3) 2 = 0 ⇒ a = 3 ⇒ b = 4

Rejecting –ve values , therefore a = 3 , b = 4

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