1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.2,19 (MCQ) - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

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Ex 6.2, 19 The interval in which 𝑦 = π‘₯2 𝑒^(–π‘₯) is increasing is (A) (– ∞, ∞) (B) (– 2, 0) (C) (2, ∞) (D) (0, 2)Let f(π‘₯) = π‘₯^2 𝑒^(βˆ’π‘₯) Finding f’(𝒙) f’(π‘₯) = (π‘₯^2 𝑒^(βˆ’π‘₯) )β€² Using product rule f’(π‘₯) = (π‘₯2)β€² 𝑒^(βˆ’π‘₯) + (𝑒^(βˆ’π‘₯) )’ (π‘₯2) f’(π‘₯) = (2π‘₯) 𝑒^(βˆ’π‘₯) + (γ€–βˆ’π‘’γ€—^(βˆ’π‘₯) ) (π‘₯2) f’(π‘₯) = 2π‘₯ 𝑒^(βˆ’π‘₯)βˆ’π‘’^(βˆ’π‘₯) π‘₯2 f’(𝒙) = 𝒙 e –𝒙 (πŸβˆ’π’™) Putting f’(𝒙)=𝟎 𝒙 e –𝒙 (πŸβˆ’π’™)=𝟎 π‘₯ (2βˆ’π‘₯) = 0 So, π‘₯=0 & π‘₯ = 2 Plotting points on real line (As e –π‘₯ is always positive for all π‘₯ ∈ R) Hence, f(π‘₯) is strictly increasing on (0 , 2) Therefore, correct answer is (𝐃)
  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

    3. Ex 6.2

    Ex 6.3 →
Ex 6.3 →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo