Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If f(x) = sin 3 x + λ sin 2 x ; – π /2 < x < π /2, then the interval in which λ should lie in order that f(x) has exactly one minima and one maxima
Text Solution
Verified by ExpertsThe correct answer is:
D
f ′ (x) = sinx cos x (3 sin x + 2 λ )
f ′ (x) = 0
⇒ sin x = 0 or cos x = 0 or sin x = 
⇒ x = 0 or sin x = 
(as cos x = 0 is not possible).
If λ = 0 then f ′ (x) ≥ 0 ⇒ no extrema,
hence λ ≠ 0
⇒ – 1 < 
< 0 or 0 < 
< 1
⇒ 0 < λ < 
or – 
< λ < 0
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If f(x) = cos π x + 10x + 3x 2 + x 3 , – 2 ≤ x ≤ 3 then absolute minimum value of f(x) is-
The function f(x) = x 5 – 5x 4 + 5x 3 – 1 has-
The function f(x) = has no extrema. if (n ∈ z)
If x exceeds by its square by the greatest possible quantity then x is-
An extreme value of the function
f(x) = (sin –1 x) 3 + (cos –1 x) 3 (–1 < x < 1) is
Let f(x) = (t + 4) 4 log (t+ 1) dt, then -