A point moves along the curve 6y=x2 in such a way that when ...

Question

A point moves along the curve 6y=x2 in such a way that when x=6thex- coordinate is increasing at a rate of 2 feet per second. How fast is the y-coordinate changing when x = 6? Is the y-coordinate increasing or decreasing when x = 6? Justify your answer.

Answer 1

It is given that dx/dt = 2 when x=6 ... using implicit differentiation you can find that dy/dt = 1/3*x*(dx/dt) = 4 at the given point in time. Since dy/dt>0, y is increasing