Ajump 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?

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.