Can someone tell me how to do this type of problem? A particle moves along the curve y=sqrt(1+x^3). As it reaches the point (2,3) the y coorindate is increasing at a rate os 4cm/s. How fast is the x coordinate of the point changing at that instant?

Answer 1

Differentiate both sides with respect to t:
dy/dt = d(sqrt(1+x^3))/dx * dx/dt
=(3x²/(2sqrt(1+x³)))*dx/dt

So given x=2,y=3 and dy/dt=3 cm/s
substitute in formula above to solve for dx/dt.

I get dx/dt=2.