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Ex 6.3

Ex 6.3, 1 Deleted for CBSE Board 2023 Exams

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Ex 6.3,7 Important Deleted for CBSE Board 2023 Exams

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Ex 6.3,9 Important Deleted for CBSE Board 2023 Exams

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Ex 6.3,11 Important Deleted for CBSE Board 2023 Exams

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Ex 6.3, 14 (i) Deleted for CBSE Board 2023 Exams

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Ex 6.3, 14 (iii) Deleted for CBSE Board 2023 Exams

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Ex 6.3, 14 (v) Deleted for CBSE Board 2023 Exams

Ex 6.3,15 Important Deleted for CBSE Board 2023 Exams

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Ex 6.3,18 Important Deleted for CBSE Board 2023 Exams

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Ex 6.3,21 Important Deleted for CBSE Board 2023 Exams

Ex 6.3,22 Deleted for CBSE Board 2023 Exams

Ex 6.3,23 Important Deleted for CBSE Board 2023 Exams

Ex 6.3,24 Important Deleted for CBSE Board 2023 Exams

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Ex 6.3,26 (MCQ) Important Deleted for CBSE Board 2023 Exams

Ex 6.3,27 (MCQ) Deleted for CBSE Board 2023 Exams

Ex 6.3,14 - Chapter 6 Class 12 Application of Derivatives - Part 4

Ex 6.3,14 - Chapter 6 Class 12 Application of Derivatives - Part 5
Ex 6.3,14 - Chapter 6 Class 12 Application of Derivatives - Part 6

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Transcript

Ex 6.3, 14 Find the equations of the tangent and normal to the given curves at the indicated points: (ii) 𝑦=𝑥4 −6𝑥3+13𝑥2 −10𝑥+5 𝑎𝑡 (1, 3) Given Curve is 𝑦=𝑥4 −6𝑥3+13𝑥2 −10𝑥+5 Differentiating w.r.t x 𝑑𝑦/𝑑𝑥=4𝑥^3−18𝑥^2+26𝑥−10 Now Point Given is (1 , 3) Finding slope of tangent at (1,3) 〖𝑑𝑦/𝑑𝑥│〗_((1 , 3) )=4(1)^3−18(1)^2+26(1)−10 =4−18+26−10 =2 ∴ Slope of tangent at (1, 3) =2 Also, We know that Slope of tangent × Slope of Normal =−1 2× Slope of Normal =−1 Slope of Normal = (−1)/( 2) Hence Slope of tangent at (1 , 3)=2 & Slope of Normal at (1 , 3)=(−1)/( 2) Finding equation of tangent & normal Now Equation of line at (𝑥1 , 𝑦1) & having Slope m is 𝑦−𝑦1=𝑚(𝑥−𝑥1) Equation of tangent at (1, 3) & Slope 2 is (𝑦−3)=2(𝑥−1) 𝑦−3=2𝑥−2 𝑦=2𝑥−2+3 𝒚=𝟐𝒙+𝟏 Equation of Normal at (1, 3) & Slope (−1)/2 is (𝑦−3)=(−1)/( 2) (𝑥−1) 2(𝑦−3)=−1(𝑥−1) 2𝑦−6=−𝑥+1 2𝑦+𝑥−7=0 𝒙+𝟐𝒚−𝟕=𝟎

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