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

## (A) maximum

## (B) minimum

## (C) zero

## (D) neither maximum or minimum

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Chapter 6 Class 12 Application of Derivatives

Serial order wise

Last updated at April 16, 2024 by Teachoo

Question 14 At x = 5đ/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 = 5Ď/6 So, we will find f â (x) f (x) = 2 sin 3đĽ + 3 cos 3đĽ Finding f â (x) f â (x) = 6 cos 3đĽ â 9 sin 3đĽ Finding f ââ (x) fââ (x) = â18 sin 3đĽ â 27 cos 3đĽ At x = đđ /đ fââ (đđ /đ) = â18 sin (3(5đ/6))â 27 cos (3(5đ/6)) = â18 sin (5đ/2) â 27 cos (5đ/2) = â18 sin (2đ+đ/2) â 27 cos (2đ+đ/2) = â18 sin đ/2 â 27 cos đ/2 = â 18 (1) â 27 (0) = â18 < 0 Since fââ(x) < 0 at x = 5đ/6 â´ f has maximum at x = 5đ/6 So, the correct answer is (B)