Tangents and Normals (using Differentiation)

Question 1 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 2 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 3 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 4 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 5 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 6 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 7 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 8 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 9 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 10 Deleted for CBSE Board 2024 Exams left arrow to signify that you are on this page You are here

down arrow in sibling posts in Teachoo

Question 11 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 12 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 13 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 14 (i) Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

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

down arrow in sibling posts in Teachoo

Question 14 (iii) Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

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

down arrow in sibling posts in Teachoo

Question 14 (v) Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 15 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 16 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 17 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 18 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 19 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 20 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 21 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 22 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 23 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 24 Important Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Question 25 Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

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

down arrow in sibling posts in Teachoo

Question 27 (MCQ) Deleted for CBSE Board 2024 Exams

down arrow in sibling posts in Teachoo

Chapter 6 Class 12 Application of Derivatives
Serial order wise

Ex 6.3, 10 - Find equation of all lines having slope -1 - Ex 6.3

Ex 6.3,10 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.3,10 - Chapter 6 Class 12 Application of Derivatives - Part 3
Ex 6.3,10 - Chapter 6 Class 12 Application of Derivatives - Part 4


Transcript

Question 10 Find the equation of all lines having slope –1 that are tangents to the curve 𝑦=1/(𝑥 − 1) , 𝑥≠1.Equation of Curve is 𝑦=1/(𝑥 − 1) Slope of tangent is 𝑑𝑦/𝑑𝑥 𝑑𝑦/𝑑𝑥=𝑑(1/(𝑥 − 1))/𝑑𝑥 (𝑑𝑦 )/𝑑𝑥 =(𝑑 )/𝑑𝑥 (𝑥−1)^(−1) (𝑑𝑦 )/𝑑𝑥 =−1〖 × (𝑥−1)〗^(−1−1) (𝑑𝑦 )/𝑑𝑥 =−(𝑥−1)^(−2) 𝑑𝑦/𝑑𝑥=(− 1)/(𝑥 − 1)^2 Given that slope = −1 Hence, 𝑑𝑦/𝑑𝑥 = −1 ∴ (− 1)/(𝑥 − 1)^2 =−1 1/(𝑥 − 1)^2 =1 1=(𝑥 − 1)^2 (𝑥 − 1)^2=1 𝑥 − 1=±1 x − 1 = 1 x = 2 x − 1 = −1 x = 0 So, x = 2 & x = 0 Finding value of y If x = 2 y = 1/(𝑥 − 1) y = 1/(2 − 1) y = 1/1 y = 1 Thus, point is (2, 1) If x = 0 y = 1/(𝑥 − 1) y = 1/(0 − 1) y = 1/(−1) y = −1 Thus, point is (0, –1) Thus, there are 2 tangents to the curve with slope 2 and passing through points (2, 1) and (0, −1) We know that Equation of line at (𝑥1 , 𝑦1)& having Slope m is 𝑦−𝑦1=𝑚(𝑥−𝑥1) Equation of tangent through (2, 1) is 𝑦 −1 =−1 (𝑥 −2) 𝑦 −1 =−𝑥+2 𝒚+𝒙−𝟑 = 𝟎 Equation of tangent through (0, −1) is 𝑦 −(−1)=−1 (𝑥 −0) 𝑦 +1 =−𝑥 𝒚+𝒙 + 𝟏 = 𝟎

Go Ad-free
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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.