A particle moves along the curve y = sqr(1+x^3). As it reaches the point (2,3), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instant.

Answer 1

y = √(1+x^3)
dy/dt = 3x^2 / 2√(1+x^3) dx/dt
4 = 3*4 / 2*3 dx/dt
dx/dt = 2