Question

A particle moves along the curve y = 5x2 - 1 in such a way that the y value is decreasing at the rate of 2 units per second. At what rate is x changing when x = 1.

Answer 1

Given

y = 5x² - 1

differentiating both sides with respect to time t yields

dy/dt = 10x dx/dt

We're told that y decreases at a rate of 2 units/s, which means dy/dt = -2. At the moment x = 1, we have

-2 = 10•1 dx/dt   ⇒   dx/dt = -2/10 = -1/5

which is to say, the x value decreases at a rate of 1/5 units/s.