Example 8 - Show f(x) = x3 - 3x2 + 4x is strictly increasing

Example 8 - Chapter 6 Class 12 Application of Derivatives - Part 2

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

Transcript

Example 8 Show that the function f given by f (๐‘ฅ) = ๐‘ฅ3 โ€“ 3๐‘ฅ2 + 4๐‘ฅ, ๐‘ฅ โˆˆ R is strictly increasing on R. f(๐‘ฅ) = ๐‘ฅ3 โ€“ 3๐‘ฅ2 + 4๐‘ฅ Finding fโ€™(๐’™) fโ€™(๐‘ฅ) = 3๐‘ฅ2 โ€“ 3.2๐‘ฅ + 4 fโ€™(๐‘ฅ) = 3x2 โ€“ 6๐‘ฅ + 4 fโ€™(๐‘ฅ) = 3x2 โ€“ 6๐‘ฅ + 3 + 1 fโ€™(๐‘ฅ) = 3 (๐‘ฅ2 โ€“ 2๐‘ฅ + 1) + 1 fโ€™(๐’™) = 3 (๐’™ โ€“ 1)2 + 1 As square is a positive number, The value of fโ€™(๐‘ฅ) will be always positive for every real number Hence fโ€™(๐’™) > 0 for all ๐‘ฅ โˆˆ R โˆด f(๐‘ฅ) is strictly increasing

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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.