# Example 16 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 16 Find the equation of all lines having slope 2 and being tangent to the curve y + 2𝑥 − 3 = 0 The curve is y + 2𝑥−3 = 0 Slope of the tangent to the curve at point (x, y) is 𝑑𝑦 𝑑𝑥 𝑑𝑦 𝑑𝑥 + 𝑑 𝑑𝑥2𝑥 − 3=0 𝑑𝑦 𝑑𝑥 =− 𝑑 𝑑𝑥2𝑥 − 3 𝑑𝑦 𝑑𝑥 =− 0𝑥 − 3 − 21𝑥 − 32 𝑑𝑦 𝑑𝑥 =− −2𝑥 − 32 𝑑𝑦 𝑑𝑥 =2𝑥 − 32 Given that slope = 2 Hence, 𝑑𝑦𝑑𝑥 = 2 2𝑥 − 32=2 1𝑥 − 32=1 𝑥−32 = 1 So, x – 3 = ±1 So, x = 4 & x = 2 Finding value of y Thus, there are 2 tangents to the curve with slope 2 and passing through points (2, 2) and (4, − 2)

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Chapter 6 Class 12 Application of Derivatives

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About the Author

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.