Question 26 The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is (A) 3 (B) 1/3 (C) – 3 (D) – 1/3Slope of tangent is 𝑑𝑦/𝑑𝑥 𝑦=2𝑥^2+3 sin⁡𝑥 Differentiating w.r.t. 𝑥 𝑑𝑦/𝑑𝑥=𝑑(2𝑥^2 +3 sin⁡𝑥 )/𝑑𝑥 𝑑𝑦/𝑑𝑥=4𝑥+3 cos⁡𝑥 We know that Slope of tangent × Slope of Normal =−1 (4𝑥+3 cos⁡𝑥 ) × Slope of Normal =−1 Slope of Normal = (−1)/(4𝑥 + 3 cos⁡𝑥 ) We need to find Slope of Normal at 𝑥=0 At x = 0 Slope of Normal =(− 1 )/(4(0) + 3 cos⁡〖0°〗 ) =(−1)/(0 + 3(1) )=(−1)/( 3) Hence, Correct Answer is D

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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