Lets look at how differentiation can be used to solve real life problems. Here are two worked examples that illustrate such problems.

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Worked Example

You have \(120\) m of fencing and want to make two enclosures as shown in the diagram. The problem is to maximise the area, A, enclosed.

Use the fact that the total length of fencing is \(\120) m to write an equation connecting \(x\) and \(y\).

Make \(y\) the subject of this equation and hence write a formula for A in terms of \(x\).

Now differentiate with respect to \(x\) and put it equal to zero to solve the problem.
Worked Example

A closed cylindrical can has a volume of \(350 cm^{3}\). Find the dimensions of the can that minimise the surface area.

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