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. 311 questions 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, 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.
