Monday

April 21, 2014

April 21, 2014

Posted by **Melinda** on Friday, December 9, 2011 at 9:20pm.

Maximum:3

Minimum:1

Is this a valid reason:

A quartic polynomial function has a 3 Turning points. The turning point is always 1 less than the degree. For example degree 4=3 TP, degree 5=4 turning points?

What about the minimum?

- Math -
**Reiny**, Friday, December 9, 2011 at 11:03pmIf the x^4 term is positive, then the curve rises in the 1st and 2nd quadrants, so there has to be at least one minimum point.

if the x4 term is negative, then the curve drops down in the 3rd and 4th quadrants, and there has to be at least one maximum.

For yours the curve will be downwards, so it could look like an upside down W

Draw a WW. You will see that there are 2 mins and 1 max if it opens up, and if the curve looks like an M, (-x^4), there could be 2 max's and 1 min

There cannot be 3 max's and 1 min for a quartic

Your statement about the turning points is correct, but those turning points could be maximums or minimums

I will give you a few examples of equations where it is obvious, I will leave the equations in factored form

1. y = (x+1)(x+2)(x-3)(x+4)

The curve opens up , and has x-intercepts at

x = -1,-2,3, and 4 , so it is easy to see that there must be 2 mins and 1 max

2. y = (x-2)(x-3)(x^2 + 4)

http://www.wolframalpha.com/input/?i=+%28x-2%29%28x-3%29%28x%5E2+%2B+4%29%3D0

3. y = (x-10)(x^3-3)

http://www.wolframalpha.com/input/?i=+%28x-10%29%28x%5E3-3%29%3D0

Play around with different quartics on this webpage, and you can see the different cases.

try:

y = x^4

y = x^4 + x^3

y = x^4 + x^3 + x^2

etc

now change some of the signs .

Have some fun with math.

**Related Questions**

precalculus - Determine the maximum and minimum number of turning points for the...

Precalculus - Number of possible turning points in the following equation f(x)=...

Functions - Determine the maximum possible number of turning points for the ...

math pre calculus - find the following for the function f(x)=(x+5)^2(x-2)^2 a....

math - what is the number of noncollinear points that determine a cirlce ...

math (someone please help me!) - f(x)=((x+1)^3)-2 -Determine the number of ...

Algebra- Maximum and minimum. - I dont understand how to find the maximum and ...

Functions/End behavior - f(x)=x^2(x^2-2)(x+2) Determine the end behavior, find ...

Math - I really really need help on this one. I have no clue on how to do it; ...

precalculus - analyze the graph of f(x)=(x+3)x-1)^2 x and y itercepts; end ...