Ex 6.2,19 - Chapter 6 Class 12 Application of Derivatives (Term 1)
Last updated at Aug. 9, 2021 by Teachoo
To show increasing/decreasing in intervals
Last updated at Aug. 9, 2021 by Teachoo
Ex 6.2, 19 The interval in which π¦ = π₯2 π^(βπ₯) is increasing is (A) (β β, β) (B) (β 2, 0) (C) (2, β) (D) (0, 2)Let f(π₯) = π₯^2 π^(βπ₯) Finding fβ(π) fβ(π₯) = (π₯^2 π^(βπ₯) )β² Using product rule fβ(π₯) = (π₯2)β² π^(βπ₯) + (π^(βπ₯) )β (π₯2) fβ(π₯) = (2π₯) π^(βπ₯) + (γβπγ^(βπ₯) ) (π₯2) fβ(π₯) = 2π₯ π^(βπ₯)βπ^(βπ₯) π₯2 fβ(π) = π e βπ (πβπ) Putting fβ(π)=π π e βπ (πβπ)=π π₯ (2βπ₯) = 0 So, π₯=0 & π₯ = 2 Plotting points on real line (As e βπ₯ is always positive for all π₯ β R) Hence, f(π₯) is strictly increasing on (0 , 2) Therefore, correct answer is (π)