Question 2 - Examples - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Question 2 Find the point at which the tangent to the curve 𝑦 = √(4𝑥−3)−1 has its slope 2/3 . Given, Slope of the tangent to the curve is 2/3 We know that Slope of tangent = 𝒅𝒚/𝒅𝒙 2/3 = 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 2/3 𝑑(√(4𝑥 − 3) − 1)/𝑑𝑥 = 2/3 1/(2√(4𝑥 − 3)) ×4−0 = 2/3 2/√(4𝑥 − 3) = 2/3 3 = √(4𝑥−3) √(𝟒𝒙−𝟑) = 3 Squaring both sides 4x − 3 = 9 4x = 12 x = 3 Finding y for x = 3 𝑦=√(4𝑥−3) − 1 =√(12−3)−1 =√9−1 =3−1 =𝟐 Hence, the required point is (𝟑, 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo