Last updated at May 6, 2021 by Teachoo

Transcript

Example 7 (Method 1) Show that the function given by f (๐ฅ) = 7๐ฅ โ 3 is strictly increasing on R.f(๐ฅ) = 7๐ฅ โ 3 Finding fโ(๐) fโ(x) = (7x โ 3)โ fโ(x) = 7 Since fโ(๐) > 0 Hence, f is strictly increasing on R Example 7 (Method 2 ) Show that the function given by f (x) = 7x โ 3 is strictly increasing on R. Let ๐ฅ1 and ๐ฅ2 be real numbers Such that ๐๐ < ๐2 Multiplying both sides by 7 7๐ฅ1 < 7๐ฅ2 Subtracting both sides by 3 7๐ฅ1 โ 3 < 7๐ฅ2 โ 3 f (๐๐) < f ( ๐2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.

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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.