Ex 6.2, 13 On which intervals f (x) = x100 + sin ⁡x -1 strictly - Ex 6.2

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  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.2,13 On which of the following intervals is the function f given by f ( ) = 100 + sin 1 strictly decreasing ? (A) (0,1) (B) 2 , (C) 0, 2 (D) None of these f (x) = 100 + sin x 1 f (x) = 100 99 + cos x (A) (0, 1) For 0 < x < 1 So, 100 x99 + cos x is positive. f (x) > 0 f (x) is increasing on (0, 1) (B) , 2 < x < 1.57 < x < 3.14 Since 100 x99 is much greater than 1 So 100 x99 + cos x is positive f (x) > 0 , 0< < 2 So 100 x99 + cos x is positive f (x) > 0 f(x) is increasing on 0, 2 f(x) is strictly decreasing for none of the intervals. So (D) is the correct answer

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