can someone tell me what is the difference between a relative max. or min. and an absolute max or min value?

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- January 24th 2010, 06:49 PMkattdifferences
can someone tell me what is the difference between a relative max. or min. and an absolute max or min value?

- January 24th 2010, 07:06 PMVonNemo19
Relative Max: Let be a critical number of a function .

1. If from negative to postive at , then has a relative minimum at

2.If from positive to negative at , then has a relative maximum at

Now let

3. Suppose that is defined over the interval and . Then, if for all , is an absolute maximum for on - January 25th 2010, 03:56 AMHallsofIvy
A function, f, has an

**absolute**minimum at x= a if f(a) is less than or equal to any value of f(x).

A function, f, has a**relative**minimum at x= a if f(a) is less than or equal to any value of f(x)**on some small interval around a**.

For absolute and relative maximum switch "less than" to "larger than".

What VonNemo19 said about relative maximum and minimum is true for**differentiable**functions.

But the function f(x)= x for all x except 1, f(1)= 2, has a relative maximum at x= 1 even though the derivative, where ever it is defined, never changes sign