Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12



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


Ex 6.3, 11 Find the equation of all lines having slope 2 which are tangents to the curve ๐‘ฆ=1/(๐‘ฅ โˆ’ 3) , ๐‘ฅโ‰ 3. The Equation of Given Curve is : ๐‘ฆ=1/(๐‘ฅ โˆ’ 3) We know that Slope of tangent is ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘(1/(๐‘ฅ โˆ’ 3))/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘‘/๐‘‘๐‘ฅ (๐‘ฅโˆ’3)^(โˆ’1) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(โˆ’1) (๐‘ฅโˆ’3)^(โˆ’1โˆ’1) . ๐‘‘(๐‘ฅ โˆ’ 3)/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=โˆ’(๐‘ฅโˆ’3)^(โˆ’2) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=(โˆ’1)/(๐‘ฅ โˆ’ 3)^2 Given that slope = 2 Hence, ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 2 โˆด (โˆ’1)/(๐‘ฅ โˆ’ 3)^2 =2 โˆ’1=2(๐‘ฅโˆ’3)^2 ใ€–2(๐‘ฅโˆ’3)ใ€—^2=โˆ’1 (๐‘ฅโˆ’3)^2=(โˆ’1)/( 2) We know that Square of any number is always positive So, (๐‘ฅโˆ’3)^2>0 โˆด (๐‘ฅโˆ’3)^2=(โˆ’1)/( 2) not possible Thus, No tangent to the Curve has Slope 2

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.