Question

A point on the graph of y = 1/x is moving along the curve in such a way that its x-coordinate is increasing at a rate of 3 units per second. What is happening to the y-coordinate at the instant the y-coordinate is equal to 2

Answer 1

y = 1/x
dy/dx = -1/x^2 dx/dt = -1/x^2 (3) = -3/x^2

dy/dt = dy/dx * dx/dt = -3/x^2 * 3 = -9/x^2

When y = 2,
2 = 1/x
x = 1/2

dy/dt = -9/(1/2)^2 =-9/(1/4) = -36

Therefore, at y = 2, the y-coordinate is decreasing at a rate of 36 units per seconds.