# Ex 6.3,15

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 6.3,15 Find the equation of the tangent line to the curve = 2 2 +7 which is : (a) parallel to the line 2 +9=0 We know that Slope of tangent is = 2 2 +7 Differentiating w.r.t. =2 2 Finding Slope of line 2 +9=0 2 +9=0 =2 +9 =2 +9 The Above Equation is of the form = + where m is Slope of line Hence Slope of line 2 +9 is 2 Now, Given tangent is parallel to 2 +9=0 Slope of tangent = Slope of line 2 +9 = 0 =2 2 2=2 2 1 =2 =2 Finding y when =2 , = 2 2 +7= 2 2 2 2 +7=4 4+7=7 We need to find Equation of tangent passes through 2 , 7 & Slope is 2 Equation of tangent is 7 =2 2 7=2 4 2 7+4=0 2 3=0 Hence Required Equation of tangent parallel to = Ex 6.3,15 Find the equation of the tangent line to the curve = 2 2 +7 which is (b) perpendicular to the line 5 15 =13 We know that Slope of tangent is = 2 2 +7 Differentiating w.r.t. =2 2 Finding Slope of line 5 15 =13 5 15 =13 5 =15 +13 = 1 5 15 +13 = 15 5 + 13 5 =3 + 13 5 Above Equation is of the form = + , where m is Slope of a line Slope = 3 Now, Given tangent is perpendicular to 5 15 =13 Slope of tangent Slope of line = 1 3= 1 = 1 3 2 2= 1 3 2 = 1 3 +2 2 = 1 + 6 3 2 = 5 3 = 5 6 Finding y when = 5 6 = 2 2 +7= 5 6 2 2 5 6 +7= 25 36 10 6 +7= 217 36 Point is 5 6 , 217 36 Equation of tangent passing through 5 6 , 217 36 & having Slope 1 3 217 36 = 1 3 5 6 36 217 36 = 1 3 5 6 36 217= 36 3 5 6 36 217= 12 5 6 36 217= 12 + 12 5 6 36 217= 12 +10 36 217= 12 +10 36 +12 217 10=0 + = is Required Equation of tangent

Chapter 6 Class 12 Application of Derivatives

Ex 6.3,5
Important

Ex 6.3,7 Important

Ex 6.3,12 Important

Ex 6.3,15 Important You are here

Ex 6.3,26 Important

Example 35 Important

Example 37 Important

Example 38 Important

Example 40 Important

Ex 6.5,1 Important

Ex 6.5,5 Important

Ex 6.5,7 Important

Ex 6.5,11 Important

Ex 6.5,18 Important

Ex 6.5,20 Important

Ex 6.5,23 Important

Ex 6.5,26 Important

Ex 6.5,28 Important

Example 46 Important

Example 47 Important

Misc 6 Important

Misc 11 Important

Misc 13 Important

Misc 17 Important

Misc 22 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.