Question

A particle moves along the curve y = 4x2 + 1 in such a way that the x value is increasing at the rate of 2 units per second. At what rate is y changing when x = 1?.

Answer 1

By differentiating both sides of y = 4x² + 1 with respect to time t, we have

dy/dt = 8x dx/dt

If the x value changes at a rate of +2 units/second (that is, dx/dt = 2) at the moment x = 1, then the y value changes at a rate of

dy/dt = 8 • 1 • 2 units/s = 16 units/s