Let f(x) = & x ∈ Then the interval in which at least one …

Maths Differentiation and Applications of Derivatives General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f(x) = & x ∈

Then the interval in which at least one root of equaiton lie + + = 0

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a, d)

f '(x) =

Let g(x) = sin x – x cos x

g'(x) = cos x + x sin x – cos x

g'(x) > 0 ∀ x ∈ (0, π /2)

g(x)

g(0) < g(x)

0 < sin x – x cos x

∴ f '(x) > 0

f(x) Let α = π /12, β = π /4, r = 5 π /12

⇒ f( α ) < f( β ) < f(r)

Let H(x) = 2 (x –f( β )) (x – f(r)) + 3 (x – f( α )) (x – f(r)) + 4 (x – f( α )) (x – f( β ))

H (f(r)) > 0, H(f( β )) < 0, H(f(r)) > 0

⇒ one root in (f(r), f( β ))

and other in (f( β ), f(r))

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.