Question

A particle moves along the curve x^2+4=y. The point on the curve at which the y coordinate changes twice as fast as the x coordinate,is

Answer 1

you want dy/dt = 2 dx/dt

x^2+4 = y
2x dx/dt = dy/dt

So, you want 2x dx/dt = 2 dx/dt
2x = 2
x = 1

So, at (1,5) dy/dt = 2 dx/dt

or, you want dy/dx = 2
y = x^2+4
dy/dx = 2x = 2
x = 1