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

Last updated at Dec. 16, 2024 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

Slide105.JPG

Slide106.JPG
Slide107.JPG

Share on WhatsApp

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo