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 Dec. 13, 2024 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

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

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