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 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.
