A curve, representing the vertical cross-section of a high-precision optical lens, has the equation y=2x3−96xy = 2x^3 - 96xy=2x3−96x.
The point PPP on the curve has xxx-coordinate 444.
The point QQQ on the curve has xxx-coordinate 4+h4 + h4+h.
Show that the gradient of the chord PQPQPQ is 2h2+24h2h^2 + 24h2h2+24h.
Explain how the result of part (a) can be used to show that PPP 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.
