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Ex 6.2, 1 - Show that f(x) = 3x + 17 is strictly increasing - To show increasing/decreasing in whole domain

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Ex 6.2,1(Method 1) Show that the function given by f (๐‘ฅ) = 3๐‘ฅ + 17 is strictly increasing on R. f(๐‘ฅ) = 3๐‘ฅ + 17 fโ€™ (๐‘ฅ) = 3 value of fโ€™ (๐‘ฅ) is positive for all real number Hence fโ€™ (๐‘ฅ) = positive for all ๐‘ฅ โˆˆ R f is strictly increasing on R Ex 6.2,1(Method 2) Show that the function given by f (x) = 3x + 17 is strictly increasing on R. Let ๐‘ฅ1 and ๐‘ฅ2 be real numbers Such that ๐‘ฅ1 < ๐‘ฅ2 Multiplying both sides by 3 3๐‘ฅ1 < 3 ๐‘ฅ2 Adding both sides by 3 3๐‘ฅ1 + 17 < 3๐‘ฅ2 + 17 f (๐‘ฅ1) < f ( ๐‘ฅ2) Hence if ๐‘ฅ1 < ๐‘ฅ2 Then f (๐‘ฅ1) < f (๐‘ฅ2) Hence f is strictly increasing on R

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