Question 14 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at August 12, 2026 by

At x = 5π/6, f (x) = 2 sin 3x + 3 cos 3x is :

(A) maximum 

(B) minimum

(C) zero 

(D) neither maximum or minimum

At x = 5π/6, f (x) = 2 sin3x + 3 cos3x is: - Teachoo Maths [MCQ] - NCERT Exemplar - MCQs

part 2 - Question 14 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives
part 3 - Question 14 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives

Remove Ads Take short quiz All Quiz and Worksheets
Teachoo · Class 12 Explore Class 12

Transcript

Question 14 At x = 5𝜋/6, f (x) = 2 sin 3x + 3 cos 3x is : maximum (B) minimum (C) zero (D) neither maximum or minimum Since, we have to check maximum and minimum value at x = 5π/6 So, we will find f ” (x) f (x) = 2 sin 3𝑥 + 3 cos 3𝑥 Finding f ’ (x) f ’ (x) = 6 cos 3𝑥 − 9 sin 3𝑥 Finding f ’’ (x) f’’ (x) = −18 sin 3𝑥 − 27 cos 3𝑥 At x = 𝟓𝝅/𝟔 f’’ (𝟓𝝅/𝟔) = −18 sin (3(5𝜋/6))− 27 cos (3(5𝜋/6)) = −18 sin (5𝜋/2) − 27 cos (5𝜋/2) = −18 sin (2𝜋+𝜋/2) − 27 cos (2𝜋+𝜋/2) = −18 sin 𝜋/2 − 27 cos 𝜋/2 = − 18 (1) − 27 (0) = −18 < 0 Since f’’(x) < 0 at x = 5𝜋/6 ∴ f has maximum at x = 5𝜋/6 So, the correct answer is (B)

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.