# Ex 6.2,13 - Chapter 6 Class 12 Application of Derivatives

Last updated at Jan. 7, 2020 by Teachoo

Last updated at Jan. 7, 2020 by Teachoo

Transcript

Ex 6.2,13 On which of the following intervals is the function f given by f (π₯) = π₯^100 + sinβ‘π₯ β1 strictly decreasing ? (A) (0, 1) (B) (π/2, π) (C) (0, π/2) (D) None of these f (x) = π₯100 + sin x β 1 fβ(x) = 100π₯99 + cos x (A) (0, 1) For 0 < x < 1 0 < x < 1.57 099 < x99 < (1.57)99 0 < x99 < 2.47 Γ 1099 0 < 100x99 < 247 Γ 1019 0 < x < 1 β΄ 0 < x < π/2 So x is in 1st quadrant β΄ cos x is positive (As π/2 = 3.14/2 = 1.57 > 1) So, 100 x99 + cos x is positive. β΄ fβ(x) > 0 f (x) is increasing on (0, 1) (B) (π /π, π ) π/2 < x < π 1.57 < x < 3.14 Since 100 x99 is much greater than β1 So 100 x99 + cos x is positive β΄ fβ (x) > 0 1.57 < x < 3.14 (1.57)99 < x99 < (3.14)99 2.47 Γ 1099 < x99 < 3.14 Γ 1099 247 Γ 1099 < 100 x99 < 314 Γ 1099 Since π/2 < x < π so x is in 2nd quadrant β΄ cos x is negative. Minimum value of cos x = β1 (πͺ)(π, π /π) 0<π₯< π/2 So 100 x99 + cos x is positive β΄ fβ (x) > 0 f(x) is increasing on (0,π/2) 0<π₯< π/2 0 < x < 1.57 099 < x99 < (1.57)99 0 < x99 < 2.47 Γ 1099 0 < cos x < π/2 So x is in 1st quadrant β΄ cos x is positive Thus, f(x) is strictly decreasing for none of the intervals. So, (D) is the correct answer

Chapter 6 Class 12 Application of Derivatives

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.