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.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
