Example 8 - Chapter 6 Class 12 Application of Derivatives (Term 1)
Last updated at May 6, 2021 by Teachoo
Transcript
Example 8 Show that the function f given by f (๐ฅ) = ๐ฅ3 โ 3๐ฅ2 + 4๐ฅ, ๐ฅ โ R is strictly increasing on R. f(๐ฅ) = ๐ฅ3 โ 3๐ฅ2 + 4๐ฅ Finding fโ(๐) fโ(๐ฅ) = 3๐ฅ2 โ 3.2๐ฅ + 4 fโ(๐ฅ) = 3x2 โ 6๐ฅ + 4 fโ(๐ฅ) = 3x2 โ 6๐ฅ + 3 + 1 fโ(๐ฅ) = 3 (๐ฅ2 โ 2๐ฅ + 1) + 1 fโ(๐) = 3 (๐ โ 1)2 + 1 As square is a positive number, The value of fโ(๐ฅ) will be always positive for every real number Hence fโ(๐) > 0 for all ๐ฅ โ R โด f(๐ฅ) is strictly increasing
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About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.