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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
