Edexcel Further Pure Maths IGCSE (2017) SAM Paper 2 Q10

Titanic 18 mark cartesian co-ordinates question.
The method:
-Differentiate to find the gradient and use substitution to find the Y-coordinate of the point P which the tangent line L1 passes through
-Solve for x when dy/dx = -1 to find the other x-coordinate on the graph which has the same gradient
-Find the normal such that m(normal) * dy/dx = -1 and it passes through the point P, then find the point R by letting the y of L2 be equal to the y of the normal and solving for x, then use substitution to find the y-coordinate of R
-Use pythagoras' theorem and the difference in y and x values to find the distance PR
-Use the same technique to find the distance QR then take the area as the base times height or PR x QR of the rectangle

This question is mainly relevant to
Topic 8 : Rectangular Cartesian Coordinates
Topic 9 : Calculus

This question is somewhat relevant to
Topic 4 : Graphs
Topic 2 : The Quadratic Equation