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

The webmaster and author of the Math Help site is Graeme McRae.
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