## Definition of a Critical Number

Let f be defined at c. If f'(c) = 0 or f' is undefined at c, then c is
a **critical number** of f.

**Why is this important?**

Because relative
extrema occur only at critical numbers. The way to find the maximum
and minimum of a function, f, on an interval [a,b] is to find the value of f at
each critical number and at the two endpoints of the interval. The largest
value obtained this way is the maximum of f, and the smallest is its minimum.

### Related pages in this website

Relative
Extrema Occur Only at Critical Numbers -- if c is an extremum then f'(c)=0
or f'(c) is undefined

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Graeme McRae.