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.
717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.