Question 22 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Feb. 10, 2025 by Teachoo

Find the interval/s in which the function f:R→R defined by f(x)=xe^x, is increasing

This question is similar to Ex 6.2 ,19 Chapter 6 Class 12

Find the intervals in which function f(x) = xe^x is increasing [Video] - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 22 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 22 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

Let f(𝑥) = 𝑥𝑒^𝑥 Finding f’(𝒙) f’(𝑥) = (𝑥𝑒^𝑥 )′ Using product rule f’(𝑥) = (𝑥)′ 𝑒^𝑥 + (𝑒^𝑥 )’ (𝑥) f’(𝑥) = (1) 𝑒^𝑥 + (𝑒^𝑥 ) (𝑥) f’(𝑥) = 𝑒^𝑥+𝑒^𝑥 𝑥 f’(𝒙) = e 𝒙 (𝟏+𝒙) Putting f’(𝒙)=𝟎 e 𝒙 (𝟏+𝒙) =𝟎 1+𝑥 = 0 So, 𝑥=−1 Plotting points on real line Hence, f(𝑥) is increasing on [−𝟏 ,∞)

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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 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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