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 August 14, 2026 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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