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Ex 6.2, 18 Prove that the function given by f (๐‘ฅ) = ๐‘ฅ3 โ€“ 3๐‘ฅ2 + 3๐‘ฅ โ€“ 100 is increasing in R. We need to show f(๐‘ฅ) is strictly increasing on R i.e. we need to show fโ€™(๐’™) > 0 Finding fโ€™(๐’™) fโ€™(๐‘ฅ)= 3x2 โ€“ 6x + 3 โ€“ 0 = 3(๐‘ฅ2โˆ’2๐‘ฅ+1) = 3((๐‘ฅ)2+(1)2โˆ’2(๐‘ฅ)(1)) = 3(๐‘ฅโˆ’1)2 Since Square of any number is always positive (๐‘ฅโˆ’1)2 > 0 3(๐‘ฅโˆ’1)2>0 fโ€™(๐’™) > 0 Hence, fโ€™(๐‘ฅ) > 0 for all values of ๐‘ฅ โˆด f(๐‘ฅ) is strictly increasing on R

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

About the Author

Davneet Singh

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