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
CBSE Class 12 Sample Paper for 2024 Boards
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CBSE Class 12 Sample Paper for 2024 Boards
Last updated at April 16, 2024 by Teachoo
This question is similar to Ex 6.2 ,19 Chapter 6 Class 12
Let f(đĽ) = đĽđ^đĽ Finding fâ(đ) fâ(đĽ) = (đĽđ^đĽ )â˛ Using product rule fâ(đĽ) = (đĽ)â˛ đ^đĽ + (đ^đĽ )â (đĽ) fâ(đĽ) = (1) đ^đĽ + (đ^đĽ ) (đĽ) fâ(đĽ) = đ^đĽ+đ^đĽ đĽ fâ(đ) = e đ (đ+đ) Putting fâ(đ)=đ e đ (đ+đ) =đ 1+đĽ = 0 So, đĽ=â1 Plotting points on real line Hence, f(đĽ) is increasing on [âđ ,â)