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Ex 6.3, 11 - Find equation of all lines having slope 2 which - Finding equation of tangent/normal when slope and curve are given

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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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﷯﷯ But Given Slope of tangent =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 is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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