If an object is moving along the curve y=x^3, at what points is the y-coordinate changing 3 times more rapidly then the x-coordinate?

Answer 1

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)