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.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, 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). Each one has a worked solution and a mark scheme showing where the marks go.