Consider the hyperbola y = 1/x and think of it as a slide. A particle slides along the hyperbola so that its x-coordinate is increasing at a rate of f(x) units/sec. If its y-coordinate is decreasing at a constant rate of 1 unit/sec, what is f(x)?

Question

-I arrived at the answer f(x)= x^2 but i am not quite sure about my answer, pls help for my assigment.

Answer 1

y = 1/x
dy/dt = -1/x^2 dx/dt

-1 = -1/x^2 dx/dt
dx/dt = x^2

Looks good to me.