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1.10 G: Differentiation

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Question 176

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​−100

where PPP is measured in hundreds of pounds and £x£x£x is the selling price of each tablet.

According to this model:

a.

find, using calculus, the maximum possible weekly profit.

[4]
b.

Justify, also using calculus, that the profit you have found is a maximum.

[3]
Markscheme

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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