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 Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) 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.
