1. Chapter 6 Class 12 Application of Derivatives
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Question 11 - Tangents and Normals (using Differentiation) - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

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

    3. Tangents and Normals (using Differentiation)

    Approximations (using Differentiation) →
Approximations (using Differentiation) →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo