Ex 6.2, 7 - Show that y = log (1 + x) - 2x/2+x is increasing - Ex 6.2

Slide32.JPG
Slide33.JPG Slide34.JPG

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

Transcript

Ex 6.2,7 Show that = log(1 + ) 2 2 + , > 1 , is an increasing function of throughout its domain. = log 1+ 2 2 + , > 1 We need to show that y is strictly increasing function for > 1 i.e. we need to show that > 0 for > 1 Step 1: Finding = log 1+ 2 2 + = log 1 + 2 2 + = 1+ 2 2+ = 1 1 + . 1+ 2 2 + 2 + 2 2 + 2 = 1 1 + . 0+1 2 2 + 0 + 1 2 2 + 2 = 1 1 + 4 + 2 2 2 + 2 = 1 1 + 4 2 + 2 = 2 + 2 4 1 + 1 + 2 + 2 = 2 2 + 2 + 2 2 4 4 1 + 2 + 2 = 4 + 2 + 4 4 4 1 + 2 + 2 = 2 1 + 2 + 2 = 2 + 2 1 1 + Now, = 2 + 2 1 1 + Now, finding value where > 0 > 0 2+ 2 . 1 1+ > 0 1 1+ >0 This is possible only when 1 + > 0 i.e. > 1 So, > 0 for > 1 Hence proved

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.