Question

Y= sqrt(8 x^3 as it reaches the point (2, 4, the y-coordinate is increasing at a rate of 5 cm/s. how fast is the x-coordinate of the point changing at that instant?

Answer 1

Y = √8x³

dy/dt = 2√2 *  3/2 * √x * dx/dt
⇒ 5 = 2√2 * 3/2 * √2 * dx/dt
⇒ 5 = 6 dx/dt
⇒dx/dt = 5/6 cm/s

x coordinate is changing at 5/6 cm/s

Hope it helps!