Related Rate problem

A bug is moving along the parabola y = x^2. At what point on the parabola are the x-and-y coordinates changing at the same rate?

Thanks for the help.

y = x^2

dy/dt = 2x dx/dt

dx/dt = 2x dx/dt

2x dx/dt - dx/dt = 0

dx/dt (2x - 1) = 0

2x - 1 = 0

x = 1/2

y = (1/2)^2 = 1/4

(1/2, 1/4)
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OR:

y = x^2

dy/dt = 2x dx/dt


For dy/dt = dx/dt, 2x = 1, x = 1/2

y = x^2

Differentiate both sides with respect to t
dy/dt = 2x dx/dt

We need to find where on parabola dy/dt = dx/dt
dy/dt = dx/dt
2x dx/dt = dx/dt
2x = 1
x = 1/2

y = (1/2)^2 = 1/4

At point (1/2, 1/4)