Question

A particle moves along the curve y = 3x2 + 1 in such a way that the y value is increasing at the rate of 3 units per second. At what rate is x changing when x=2

Answer 1

y = 3x² + 1

Differentiate both sides with respect to t :

dy/dt = 6x dx/dt

We're given that dy/dt = +3 units/second, so when x = 2 we find

3 u/s = 6 • 2 dx/dt

dx/dt = 3/12 u/s = 1/4 u/s

which means x is increasing at a rate of 1/4 units per second.