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Last updated at Jan. 7, 2020 by Teachoo

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Ex 6.2,19 The interval in which ๐ฆ = ๐ฅ2 ๐^(โ๐ฅ) is increasing is (A) (โ โ, โ) (B) (โ 2, 0) (C) (2, โ) (D) (0, 2) Let f(๐ฅ) = ๐ฅ^2 ๐^(โ๐ฅ) Finding fโ(๐) fโ(๐ฅ) = (๐ฅ^2 ๐^(โ๐ฅ) )โฒ fโ(๐ฅ) = (๐ฅ2)โฒ e โ๐ฅ + (๐^(โ๐ฅ) )โ (๐ฅ2) fโ(๐ฅ) = (2๐ฅ) e โ๐ฅ + (ใโ๐ใ^(โ๐ฅ) ) (๐ฅ2) fโ(๐ฅ) = 2๐ฅ e-๐ฅ โ e-๐ฅ ๐ฅ2 fโ(๐ฅ) = ๐ฅ e โ๐ฅ (2โ๐ฅ) Putting fโ(๐)=๐ ๐ฅ e-๐ฅ (2โ๐ฅ) = 0 ๐ฅ (2โ๐ฅ) = 0 So, ๐ฅ=0 & ๐ฅ = 2 Plotting points on real line The points ๐ฅ = 0 & 2 divide the real line into 3 disjoint intervals i.e (โโ , 0) , (0 , 2) & (2 , โ) (As e โ๐ฅ is always positive for all ๐ฅ โ R) Hence, f(๐ฅ) is strictly increasing on (0 , 2) Therefore, correct answer is (๐)

Chapter 6 Class 12 Application of Derivatives

Concept wise

- Finding rate of change
- To show increasing/decreasing in whole domain
- To show increasing/decreasing in intervals
- Find intervals of increasing/decreasing
- Finding slope of tangent/normal
- Finding point when tangent is parallel/ perpendicular
- Finding equation of tangent/normal when point and curve is given
- Finding equation of tangent/normal when slope and curve are given
- Finding approximate value of numbers
- Finding approximate value of function
- Finding approximate value- Statement questions
- Finding minimum and maximum values from graph
- Local maxima and minima
- Minima/ maxima (statement questions) - Number questions
- Minima/ maxima (statement questions) - Geometry questions
- Absolute minima/maxima

About the Author

Davneet Singh

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.