Check sibling questions

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

(A) maximumΒ 

(B) minimum

(C) zeroΒ 

(D) neither maximum or minimum

Slide105.JPG

Slide106.JPG
Slide107.JPG

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

Question 27 At x = 5πœ‹/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 = 5Ο€/6 So, we will find f ” (x) f (x) = 2 sin 3π‘₯ + 3 cos 3π‘₯ Finding f ’ (x) f ’ (x) = 6 cos 3π‘₯ βˆ’ 9 sin 3π‘₯ Finding f ’’ (x) f’’ (x) = βˆ’18 sin 3π‘₯ βˆ’ 27 cos 3π‘₯ At x = πŸ“π…/πŸ” f’’ (πŸ“π…/πŸ”) = βˆ’18 sin (3(5πœ‹/6))βˆ’ 27 cos (3(5πœ‹/6)) = βˆ’18 sin (5πœ‹/2) βˆ’ 27 cos (5πœ‹/2) = βˆ’18 sin (2πœ‹+πœ‹/2) βˆ’ 27 cos (2πœ‹+πœ‹/2) = βˆ’18 sin πœ‹/2 βˆ’ 27 cos πœ‹/2 = βˆ’ 18 (1) βˆ’ 27 (0) = βˆ’18 < 0 Since f’’(x) < 0 at x = 5πœ‹/6 ∴ f has maximum at x = 5πœ‹/6 So, the correct answer is (B)

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.