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Ex 6.3

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Ex 6.3, 11 - Find equation of all lines having slope 2 which

Ex 6.3,11 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.3,11 - Chapter 6 Class 12 Application of Derivatives - Part 3

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Transcript

Ex 6.3, 11 Find the equation of all lines having slope 2 which are tangents to the curve 𝑦=1/(𝑥 − 3) , 𝑥≠3.The Equation of Given Curve is : 𝑦=1/(𝑥 − 3) We know that Slope of tangent is 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥=𝑑(1/(𝑥 − 3))/𝑑𝑥 𝑑𝑦/𝑑𝑥=𝑑/𝑑𝑥 (𝑥−3)^(−1) 𝑑𝑦/𝑑𝑥=(−1) (𝑥−3)^(−1−1) . 𝑑(𝑥 − 3)/𝑑𝑥 𝑑𝑦/𝑑𝑥=−(𝑥−3)^(−2) 𝑑𝑦/𝑑𝑥=(−1)/(𝑥 − 3)^2 Given that slope = 2 Hence, 𝑑𝑦/𝑑𝑥 = 2 ∴ (−1)/(𝑥 − 3)^2 =2 −1=2(𝑥−3)^2 〖2(𝑥−3)〗^2=−1 (𝑥−3)^2=(−1)/( 2) We know that Square of any number is always positive So, (𝑥−3)^2>0 ∴ (𝑥−3)^2=(−1)/( 2) not possible Thus, No tangent to the Curve has Slope 2

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.