The flight path of a search-and-rescue drone following a specific signal intensity contour is modeled by the equation
x2+2y3−12xy=0 x^2 + 2y^3 - 12xy = 0 x2+2y3−12xy=0for x,y≥0x, y \ge 0x,y≥0. The path has a stationary point at PPP in the first quadrant where the tangent to the path is horizontal.
Show that the yyy-coordinate of PPP satisfies the equation
y2(y−18)=0 y^2(y - 18) = 0 y2(y−18)=0Hence, determine the coordinates of PPP.
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.
