Finding the maximum or minimum value of a funtion to the nth degree?

[Painguy]

How do i find the maximum or minimum value of a function to the nth degree? We've only done this for a quadratic function/equation in my class, but how would u find this for a higher degree such as x^3, x^4 or x^n? Does it follow the pattern of a power function in that x^4 is similar to x^2?

 

[NascentOxygen]

Are you restricted to a domain or range for this? Is it a polynomial of degree n?

The number of times the graph of a polynomial can [potentially] cross the x-axis is equal to its degree. So something of degree 4, for example, may cross the x-axis up to 4 times. You already know that a straight line cuts just once, and a circle or parabola crosses up to two times.

As for finding local max and min without calculus, hmmm ...

 

[Painguy]

Are you restricted to a domain or range for this? Is it a polynomial of degree n?

The number of times the graph of a polynomial can [potentially] cross the x-axis is equal to its degree. So something of degree 4, for example, may cross the x-axis up to 4 times. You already know that a straight line cuts just once, and a circle or parabola crosses up to two times.

As for finding local max and min without calculus, hmmm ...

Haha I see Never mind then. I suppose i can wait until i know more. Thx for the other explanation though.

 

[verty]

Calculus is good at finding maximum and minimum values of functions, it's one of its most useful functions. Without calculus, you have to basically draw the graph or look at the form of the equation to see where the minimum value will occur. But learning about graphs will help with calculus later, because you can't rely on formulas all the time :).

 

[Windowmaker]

x^4 looks a little different from x^2, if my memory serves me correctly.

Normally a function of nth degree has at most n-1 turns.