A transport container for radioactive waste is designed as a cuboid with width xxx m, length 2.5x2.5x2.5x m, and height hhh m. The total interior volume of the container must be 500 m3500\text{ m}^3500 m3.
Show that the total surface area of the container, S m2S\text{ m}^2S m2, is given by
S=5x2+1400x S = 5x^2 + \frac{1400}{x} S=5x2+x1400Find dSdx\frac{\text{d}S}{\text{d}x}dxdS.
Hence find the value of xxx for which SSS is stationary, giving your answer to 3 significant figures.
Find d2Sdx2\frac{\text{d}^2S}{\text{d}x^2}dx2d2S and hence verify that the value of xxx found in part (c) gives a minimum value for SSS.
Calculate the minimum surface area of the container, giving your answer to 1 decimal place.
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.
