Ex 6.2, 18 - Prove that f(x) = x3 - 3x2 + 3x - 100 is increasing

Ex 6.2,18 - Chapter 6 Class 12 Application of Derivatives - Part 2

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

Transcript

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

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