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 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.
