Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Find the set of values of the parameter 'a' for which the function ;
f(x) = 8ax – a sin 6x – 7x – sin 5x increases & has no critical points for all x ∈ R, is
Text Solution
Verified by ExpertsThe correct answer is:
A
a ∈ (6, ∞ )
Sol. f(x) = 8ax – a sin 6x – 7x – sin 5x
f ′ (x) = 8a – 6a cos 6x – 7 – 5cos 5x
= 8a – 7 – 6a cos 6x – 5cos 5x
f(x) is an increasing function
f ′ (x) > 0 ∴ 8a – 7 > 6a + 5
⇒ 2a > 12
a > 6
a ∈ (6, ∞ )
──────────────────────────────────────────────────────────────────────────────────────────
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 -