The vertical profile of a section of a roller coaster track is modelled by the curve with equation y=2x3−24xy = 2x^3 - 24xy=2x3−24x, where yyy is the vertical displacement in decametres and xxx is the horizontal distance in decametres from a support pylon.
Point AAA on the track is located at horizontal distance x=2x = 2x=2.
Point BBB on the track is located at horizontal distance x=2+hx = 2 + hx=2+h.
Show that the gradient of the chord ABABAB is given by 2h2+12h2h^2 + 12h2h2+12h.
Explain how the result of part (a) can be used to show that AAA is a stationary point on the track section.
