I have a question about maximum turns on a graph. In this problem:

F(x)=2x^3-2x^2+7x-25

The maximum number of turns would be 2 right?

Since the largest exponent is 3 and you subtract 1 to get the turns?

Question

I have a question about maximum turns on a graph. In this problem:

F(x)=2x^3-2x^2+7x-25

The maximum number of turns would be 2 right?

Since the largest exponent is 3 and you subtract 1 to get the turns?

anonymous · Answer

You are correct in your logic and application. Remember though that this is the MAX and you may not actually get all of them.....

anonymous · Answer

@hullsnipe do you mean in general or in this problem?

anonymous · Answer

In general. It all depends on the multiplicity of the factors (i.e., if you have two of the same factor you will have less overall turning points).

anonymous · Answer

oh okay! Thanks for the explanation.

anonymous · Answer

@hullsnipe Also, would you be able to explain how to find focal width?

One of the problems I'm supposed to find the focal width for is x^2=12y

anonymous · Answer

degree - 1

anonymous · Answer

so yes, max is 3-1 = 2

anonymous · Answer

Standard Equation   x2 = 4py
Opens		        up or down
Focus		              (0,p)
Directrix	        y = -p
Axis		        y – axis
Focal Length	 p
Focal Width           $$\left| 4p \right|$$  

So since you are in standard form the "4p" = 12 which is the Focal Width

anonymous · Answer

Oh. Wow. I thought it was way more complicated. It makes sense now. Also, thanks for putting the focal length, saved me from asking.