A manufacturer produces a specific model of electronic tablet. The weekly profit, PPP, earned by the company is modelled by the equation
P=15x−x32−100 P = 15x - x^{\frac{3}{2}} - 100 P=15x−x23−100where PPP is measured in hundreds of pounds and £x£x£x is the selling price of each tablet.
According to this model:
find, using calculus, the maximum possible weekly profit.
Justify, also using calculus, that the profit you have found is a maximum.
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.
