Example 8 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 8 Show that the function f given by f (đĽ) = đĽ3 â 3đĽ2 + 4đĽ, đĽ â R is strictly increasing on R. f(đĽ) = đĽ3 â 3đĽ2 + 4đĽ Finding fâ(đ) fâ(đĽ) = 3đĽ2 â 3.2đĽ + 4 fâ(đĽ) = 3x2 â 6đĽ + 4 fâ(đĽ) = 3x2 â 6đĽ + 3 + 1 fâ(đĽ) = 3 (đĽ2 â 2đĽ + 1) + 1 fâ(đ) = 3 (đ â 1)2 + 1 As square is a positive number, The value of fâ(đĽ) will be always positive for every real number Hence fâ(đ) > 0 for all đĽ â R â´ f(đĽ) is strictly increasing
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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