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Last updated at April 19, 2021 by Teachoo

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Ex 6.1, 11 A particle moves along the curve 6π¦ = π₯3 +2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the π₯βcoordinate.Given that A particular Moves along the curve 6π = π3 + 2 We need to find points on the curve at which π¦ coordinate is changing 8 times as fast as the π₯ β coordinate i.e. We need to find (π₯,π¦) for which π π/π π= 8 π π/π π From (1) 6π¦ = π₯3 +2 Differentiating both sides w.r.t time π (ππ)/π π=π (π^π + π)/π π 6 ππ¦/ππ‘=π(π₯^3 )/ππ‘+π(2)/ππ‘ 6 ππ¦/ππ‘=π(π₯^3 )/ππ‘ Γ ππ₯/ππ₯+0 6 ππ¦/ππ‘=π(π₯^3 )/ππ₯ Γ ππ₯/ππ‘ 6 ππ¦/ππ‘=3π₯^2 . ππ₯/ππ‘ ππ¦/ππ‘=(3π₯^2)/6 ππ₯/ππ‘ π π/π π=π^π/π π π/π π We need to find point for which ππ¦/ππ‘= 8 ππ₯/ππ‘ Putting value of ππ¦/ππ‘ from (2) π^π/π . π π/π π=π π π/π π π₯^2/2 =8 π₯^2=8 Γ 2 π₯^2=16 π₯=Β±β16 π₯=Β± 4 π₯=4 , β4 To find points, we put values of x in our equation of curve 6π¦ = π₯3 +2 When π=π 6π¦=(4)^3+2 6π¦=64+2 6π¦=66 π¦=66/6 = 11 Point is (π , ππ) When π=β π 6π¦=(β 4)^3+2 6π¦=β 64+2 6π¦=β62 π¦=(β62)/6=(βππ)/π Point is (βπ, (βππ)/π)

Ex 6.1

Ex 6.1, 1
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Ex 6.1,2 Deleted for CBSE Board 2022 Exams

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Ex 6.1,4 Important Deleted for CBSE Board 2022 Exams

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Ex 6.1,10 Important Deleted for CBSE Board 2022 Exams

Ex 6.1,11 Important Deleted for CBSE Board 2022 Exams You are here

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Ex 6.1,15 Important Deleted for CBSE Board 2022 Exams

Ex 6.1,16 Deleted for CBSE Board 2022 Exams

Ex 6.1,17 (MCQ) Deleted for CBSE Board 2022 Exams

Ex 6.1, 18 (MCQ) Important Deleted for CBSE Board 2022 Exams

Chapter 6 Class 12 Application of Derivatives (Term 1)

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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 10 years. He provides courses for Maths and Science at Teachoo.