web analytics

Example 31 - Find local minimum value of f(x) = 3 + |x| - Local maxima and minima

Slide47.JPG
Slide48.JPGSlide49.JPG

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

Transcript

Example 31 (Method 1) Find local minimum value of the function f given by f (๐‘ฅ) = 3 + |๐‘ฅ|, ๐‘ฅ โˆˆ R. f (๐‘ฅ) = 3 + |๐‘ฅ| ๐‘ฅ โˆˆ R Since Value of ๏ท๐‘ฅ๏ทฏโ‰ฅ0 So, Minimum value of ๏ท๐‘ฅ๏ทฏ=0 โ‡’ Minimum value of f (๐‘ฅ) = 3 + Minimum value of ๏ท๐‘ฅ๏ทฏ = 3 + 0 = 3 Hence minimum value of f (๐‘ฅ) = 3 We cannot find any maximum value. Example 31 (Method 2) Find local minimum value of the function f given by f (๐‘ฅ) = 3 + |๐‘ฅ|, ๐‘ฅ โˆˆ R. f (๐‘ฅ) = 3 + |๐‘ฅ| We know that ๏ท๐‘ฅ๏ทฏ=๏ท๏ทโˆ’&๐‘ฅ, ๐‘ฅ<0๏ทฎ&๐‘ฅ, ๐‘ฅโ‰ฅ0๏ทฏ๏ทฏ Hence, f (๐‘ฅ) =๏ท๏ท3โˆ’&๐‘ฅ, ๐‘ฅ<0๏ทฎ3+๐‘ฅ, ๐‘ฅโ‰ฅ0๏ทฏ๏ทฏ ๐‘ฅ = 0 is only critical point We check sign of fโ€™ (๐‘ฅ) at ๐‘ฅ = 0 Since sign of fโ€™(x) changes from negative to positive, x = 0 is point of Maxima & f (๐‘ฅ) is Minimum at ๐‘ฅ = 0 Minimum value of f (๐‘ฅ) f (0) = 3 + |0|= 3 Thereโ€™s no Maximum value of f (๐’™) Example 31 (Method 3) Find local minimum value of the function f given by f (๐‘ฅ) = 3 + |๐‘ฅ|, ๐‘ฅ โˆˆ R. f (๐‘ฅ) = 3 + |๐‘ฅ| From graph, f (๐‘ฅ) is Minimum at ๐‘ฅ = 0 So, Minimum value of f (๐‘ฅ) = f (0) = 3

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail