Example 7 - Show that f(x) = 7x - 3 is strictly increasing

Example 7 - Chapter 6 Class 12 Application of Derivatives - Part 2

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

Transcript

Example 7 (Method 1) Show that the function given by f (๐‘ฅ) = 7๐‘ฅ โ€“ 3 is strictly increasing on R.f(๐‘ฅ) = 7๐‘ฅ 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 ๐‘ฅ1 and ๐‘ฅ2 be real numbers Such that ๐’™๐Ÿ < ๐’™2 Multiplying both sides by 7 7๐‘ฅ1 < 7๐‘ฅ2 Subtracting both sides by 3 7๐‘ฅ1 โˆ’ 3 < 7๐‘ฅ2 โˆ’ 3 f (๐’™๐Ÿ) < f ( ๐’™2) Hence, when x1 < x2 , f(x1) < f(x2) Thus, f(x) is strictly increasing on R.

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.