# Ex 6.3,7

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 6.3,7 Find points at which the tangent to the curve ๐ฆ=๐ฅ^3โ3๐ฅ^2โ9๐ฅ+7 is parallel to the x-axis Equation of Curve is ๐ฆ=๐ฅ^3โ3๐ฅ^2โ9๐ฅ+7 Differentiating w.r.t. ๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^3โ 3๐ฅ^2 โ 9๐ฅ + 7)/๐๐ฅ ๐๐ฆ/๐๐ฅ=3๐ฅ^2โ6๐ฅโ9+0 ๐๐ฆ/๐๐ฅ=3๐ฅ^2โ6๐ฅโ9 ๐๐ฆ/๐๐ฅ=3(๐ฅ^2โ2๐ฅโ3) ๐๐ฆ/๐๐ฅ=3(๐ฅ^2โ3๐ฅ+๐ฅโ3) ๐๐ฆ/๐๐ฅ=3(๐ฅ(๐ฅโ3)+1(๐ฅโ3)) ๐๐ฆ/๐๐ฅ=3(๐ฅ+1)(๐ฅโ3) Given tangent to the curve is parallel to the ๐ฅโ๐๐ฅ๐๐ i.e. the Slope of tangent = Slope of ๐ฅโ๐๐ฅ๐๐ ๐ ๐/๐ ๐=๐ 3(๐ฅ+1)(๐ฅโ3)=0 (๐ฅ+1)(๐ฅโ3)=0 Thus ๐ฅ=โ1 & ๐ฅ=3 When ๐=โ๐ ๐ฆ=๐ฅ^3โ3๐ฅ^2โ9๐ฅ+7 =(โ1)^3โ3(โ1)^2โ9(โ1)+7 =โ1โ3+9+7 =12 Point is (โ1 , 12) When ๐=๐ ๐ฆ=๐ฅ^3โ3๐ฅ^2โ9๐ฅ+7 =(3)^3โ3(3)^2โ9(3)+7 =27โ27โ27+7 =โ 20 Point is (3 , โ20) Hence , the tangent to the Curve is parallel to the ๐ฅโ๐๐ฅ๐๐ at (โ๐ , ๐๐) & (๐ , โ๐๐)

Ex 6.3,5
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Ex 6.3,7 Important You are here

Ex 6.3,12 Important

Ex 6.3,15 Important

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
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- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
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- Chapter 12 Class 12 Linear Programming
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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.