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.
717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.