1.6 Differentiation

A manufacturer produces a specific model of electronic tablet. The weekly profit, $P$ , earned by the company is modelled by the equation

x^{\frac{3}{2}} - 100

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

According to this model:

find, using calculus, the maximum possible weekly profit.

[4]

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

[3]

1.6 Differentiation Questions

A manufacturer produces a specific model of electronic tablet. The weekly profit, $P$ , earned by the company is modelled by the equation

x^{\frac{3}{2}} - 100

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

According to this model:

find, using calculus, the maximum possible weekly profit.

[4]

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

[3]