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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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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.