Calculus
posted by Daniella .
If an object is moving along the curve y=x^3, at what points is the ycoordinate changing 3 times more rapidly then the xcoordinate?

y = 3x^2
dy/dt = 6x dx/dt
but dy/dt = 3 dx/dt
3dx/dt = 6x dx/dt
3 = 6x
x = 1/2
if x=1/2, y = (1/2)^3 = 1/8
It would happen at the point (1/2 , 1/8)
Respond to this Question
Similar Questions

Calculus
A point moves along the curve y=(x2)^2 such that the x coordinate is increasing at 2 units per second. At the moment x=1, how fast is its y coordinate changing. 
calculus
A particle moves along the curve y=square sqrt 1+x^3. As it reaches the point (2,3), the ycoordinate is increasing ata a rate of 4cm/s. How fast is the xcoordinate of the point changing at that instant? 
calculus
A particle is moving along the curve below. y = sqrt(x) As the particle passes through the point (4,2), its xcoordinate increases at a rate of 4 cm/s. How fast is the distance from the particle to the origin changing at this instant? 
Calculus
A particle is moving along the curve whose equation is (xy^3)/(1+y^2)= 8/5. Assume the xcoordinate is increasing at the rate of 6 units/second when the particle is at the point (1,2). At what rate is the ycoordinate of the point … 
Calculus
A particle moves along the curve y = sqr(1+x^3). As it reaches the point (2,3), the ycoordinate is increasing at a rate of 4 cm/s. How fast is the xcoordinate of the point changing at that instant. 
Calculus
A particle moves along the curve y = sqr(1+x^3). As it reaches the point (2,3), the ycoordinate is increasing at a rate of 4cm/s. How fast is the xcoordinate of the point changing at that instant? 
Math
A particle is moving along the curve y = 4x^2 + 1 in such a way that the y coordinate is increasing at a rate of ½ units per second. At what rate is the x coordinate changing at the instant x = 2? 
calc
A particle moves along the curve below. y = sqrt(8 + x^3) As it reaches the point (2, 4), the ycoordinate is increasing at a rate of 5 cm/s. How fast is the xcoordinate of the point changing at that instant? 
Calculus
A point is moving along the curve xy=12. When the point is at (4,3), the xcoordinate decreases at the rate of 2cm/sec. How fast is the ycoordinate changing at that point? 
Calculus Reposted
A point is moving along the curve xy=12. When the point is at (4,3), the xcoordinate decreases at the rate of 2cm/sec. How fast is the ycoordinate changing at that point?