A curve has equation y=x3−27xy = x^3 - 27xy=x3−27x.
The point AAA on the curve has xxx-coordinate 333.
The point BBB on the curve has xxx-coordinate 3+h3 + h3+h.
Show that the gradient of the line ABABAB is h2+9hh^2 + 9hh2+9h.
Explain how the result of part (a) can be used to show that AAA is a stationary point on the curve.
Practise Edexcel A Level Maths 9.10 Rates of Change with exam-style questions for A Level Maths. 24 questions, 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.