The flight path of a missle follows the curve y= 2x^2-1 in such a way that the value y is decreasing at the rate of 2 meters/sec. At what rate x is changing when x= -3/2 m?

Question

The flight path of a missle follows the curve y= 2x^2-1 in such a way that the value y is decreasing at the rate of 2 meters/sec. At what rate x is changing when x= -3/2 m?

Answer 1

y = 2x² - 1

When x = -3/2, y = 2(9/4) - 1 = 7/2

dy/dt = 4x(dx/dt)

So, -2 = 4(7/2)(dx/dt)

dx/dt = -1/7