In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The cross-section of a high-tensile structural support beam is modeled by the curve defined by the equation
3y2−4xy+2x2+6x=20 3y^2 - 4xy + 2x^2 + 6x = 20 3y2−4xy+2x2+6x=20where xxx and yyy are coordinates in decimetres. The boundary of the cross-section intersects the positive xxx-axis at the point RRR.
State the coordinates of RRR.
The curve has two stationary points, PPP and QQQ, where the tangent to the curve is horizontal.
Show that, at points PPP and QQQ,
ax2+bx+c=0 ax^2 + bx + c = 0 ax2+bx+c=0where aaa, bbb and ccc are integers to be found.
Find the xxx-coordinate of point QQQ, given that xQ>0x_Q > 0xQ>0, giving your answer to 3 decimal places.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) 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.
