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A point is moving along the curve y 3 =27x.Find the interval of values of x in which ordinate changes faster than the abscissa

A point is moving along the curve y3=27x.Find the interval of values of x in which ordinate changes faster than the abscissa

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
y^3 = 27x
 
3y^2 dy = 27 dx
 
dy/dx = 9/y^2
 
we want the interval such that
 
dy > dx
 
dy/dx > 1
 
9/y^2 > 1
 
y^2 – 9
 
y belongs to ( – 3, 3) – {0}
 
when y = – 3
 
-27 = 27 x
 
x = – 1
 
similarily when y = 1, x = 1
 
x belongs to ( – 1, 1) – {0}
 
Regards
Arun

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