Question

A jump rope held stationary by two children, one at each end, hangs in a shape that can be modeled by the equation h=0.01x2-x+27 , where h is the height (in inches) above the ground and x is the distance (in inches) along the ground measured from the horizontal position of one end. How close to the ground is the lowest part of the rope?

Answer 1

Because we are finding the lowest point of the rope we have to minimize the equation h=0.01x2-x+27. We first have to find the derivative of the equation which would be h’=0.02x-1 then find the value of x when h’=0, which is x=50. Using this value to substitute for x in the original equation, we find that the lowest point of the rope is only 2 inches above ground.