# Extreme Values

1. May 18, 2008

### Macleef

Could you find the extreme values for the following equation if there isn't any restrictions?

For example,

Could you find the absolute max and min for this equation?

$$f(x) = -x^{4} + 4x^{3}$$

Or do you need the restrictions:

$$f(x) = x^2 + 16x^{-1} , 1 \leq x \leq 4$$

2. May 18, 2008

### rootX

Do you mean like ABSOLUTE MAXIMUM or MINIMUM values?

In polynomial case, it is infinite (see their graphs ).. (so you do need restrictions if you want to find some meaningful maximum or minimum values)

but there are some functions like e^(-x^2) that do have absolute maximum or minimum.. (see it's graph)

3. May 18, 2008

### Dick

A polynomial can have an absolute min or max on the real line without restrictions if it's highest power is even. As rootx said, see the graph.

4. May 18, 2008

### rootX

Ooops, I forgot about even polynomials ><