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Section3.5Optimisation

One important application of differential calculus is to find the maximum (or minimum) value of a function. This often finds real world applications in problems such as the following.

The above example is sufficiently simple that we can likely determine the answer by several different methods. In general, we will need more systematic methods for solving problems of the form

Find the maximum value of \(y = f(x)\) subject to \(a \leq x \leq b\)

To do this we need to examine what a function looks like near its maximum and minimum values.