A curve has the equation x2+xy+2y2=14x^2 + xy + 2y^2 = 14x2+xy+2y2=14
The gradient of the tangent to the curve is −13\displaystyle -\frac{1}{3}−31 at the points A A\,A and BBB.
Show that 5x−y=05x - y = 05x−y=0 at A A\,A and BBB.
Find the coordinates of A A\,A and BBB.
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.
