Tangents and Normals (using Differentiation)

Question 1 Deleted for CBSE Board 2024 Exams

Question 2 Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Question 4 Deleted for CBSE Board 2024 Exams

Question 5 Important Deleted for CBSE Board 2024 Exams

Question 6 Deleted for CBSE Board 2024 Exams

Question 7 Important Deleted for CBSE Board 2024 Exams You are here

Question 8 Deleted for CBSE Board 2024 Exams

Question 9 Important Deleted for CBSE Board 2024 Exams

Question 10 Deleted for CBSE Board 2024 Exams

Question 11 Important Deleted for CBSE Board 2024 Exams

Question 12 Deleted for CBSE Board 2024 Exams

Question 13 Deleted for CBSE Board 2024 Exams

Question 14 (i) Deleted for CBSE Board 2024 Exams

Question 14 (ii) Important Deleted for CBSE Board 2024 Exams

Question 14 (iii) Deleted for CBSE Board 2024 Exams

Question 14 (iv) Important Deleted for CBSE Board 2024 Exams

Question 14 (v) Deleted for CBSE Board 2024 Exams

Question 15 Important Deleted for CBSE Board 2024 Exams

Question 16 Deleted for CBSE Board 2024 Exams

Question 17 Deleted for CBSE Board 2024 Exams

Question 18 Important Deleted for CBSE Board 2024 Exams

Question 19 Deleted for CBSE Board 2024 Exams

Question 20 Deleted for CBSE Board 2024 Exams

Question 21 Important Deleted for CBSE Board 2024 Exams

Question 22 Deleted for CBSE Board 2024 Exams

Question 23 Important Deleted for CBSE Board 2024 Exams

Question 24 Important Deleted for CBSE Board 2024 Exams

Question 25 Deleted for CBSE Board 2024 Exams

Question 26 (MCQ) Important Deleted for CBSE Board 2024 Exams

Question 27 (MCQ) Deleted for CBSE Board 2024 Exams

Chapter 6 Class 12 Application of Derivatives
Serial order wise

Ex 6.3, 7 - Find points at which tangent is parallel to x-axis

Ex 6.3,7 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.3,7 - Chapter 6 Class 12 Application of Derivatives - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 7 Find points at which the tangent to the curve 𝑦=𝑥^3−3𝑥^2−9𝑥+7 is parallel to the x-axisEquation of Curve is 𝑦=𝑥^3−3𝑥^2−9𝑥+7 Differentiating w.r.t. 𝑥 𝑑𝑦/𝑑𝑥=𝑑(𝑥^3− 3𝑥^2 − 9𝑥 + 7)/𝑑𝑥 𝑑𝑦/𝑑𝑥=3𝑥^2−6𝑥−9+0 𝑑𝑦/𝑑𝑥=3𝑥^2−6𝑥−9 𝑑𝑦/𝑑𝑥=3(𝑥^2−2𝑥−3) 𝑑𝑦/𝑑𝑥=3(𝑥^2−3𝑥+𝑥−3) 𝑑𝑦/𝑑𝑥=3(𝑥(𝑥−3)+1(𝑥−3)) 𝑑𝑦/𝑑𝑥=3(𝑥+1)(𝑥−3) Given tangent to the curve is parallel to the 𝑥−𝑎𝑥𝑖𝑠 i.e. the Slope of tangent = Slope of 𝑥−𝑎𝑥𝑖𝑠 𝒅𝒚/𝒅𝒙=𝟎 3(𝑥+1)(𝑥−3)=0 (𝑥+1)(𝑥−3)=0 Thus 𝑥=−1 & 𝑥=3 When 𝒙=−𝟏 𝑦=𝑥^3−3𝑥^2−9𝑥+7 =(−1)^3−3(−1)^2−9(−1)+7 =−1−3+9+7 =12 Point is (−1 , 12) When 𝒙=𝟑 𝑦=𝑥^3−3𝑥^2−9𝑥+7 =(3)^3−3(3)^2−9(3)+7 =27−27−27+7 =− 20 Point is (3 , −20) Hence , the tangent to the Curve is parallel to the 𝑥−𝑎𝑥𝑖𝑠 at (−𝟏 , 𝟏𝟐) & (𝟑 , −𝟐𝟎)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

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.