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Ex 6.3, 26 - Slope of normal to y = 2x2 + 3 sin x at x = 0 is - Finding slope of tangent/normal

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  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.3,26 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﷮3﷯ Slope of tangent is 𝑑𝑦﷮𝑑𝑥﷯ 𝑦=2 𝑥﷮2﷯+3 sin﷮𝑥﷯ Differentiating w.r.t.𝑥 𝑑𝑦﷮𝑑𝑥﷯= 𝑑 2 𝑥﷮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 Slope of Normal at 𝑥=0﷯= − 1 ﷮4 0﷯+3 cos﷮0°﷯﷯= −1﷮0 + 3 1﷯﷯= −1﷮ 3﷯ Hence, Correct Answer is D

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