Extreme Values

[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:

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

 

[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)

 

[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.

 

[rootX]

Ooops, I forgot about even polynomials ><