# Thread: 14th Degree Polynomial Help!

1. ## Re: 14th Degree Polynomial Help!

I worked through hundreds and hundreds of simple functions. But I can't work it out. Please Help!

2. ## Re: 14th Degree Polynomial Help!

Then you should know to evaluate your original function at the roots of its derivative having odd multiplicity.

4. ## Re: 14th Degree Polynomial Help!

What is preventing you from evaluating the function at the roots of the derivative?

5. ## Re: 14th Degree Polynomial Help!

Originally Posted by Jeka
Sorry, I don't get it. Sorry.

Can you PLEASE do an example, on my function.
I beg you!
I agree with MarkFL2. For example, let $\displaystyle f(x) = x^3 - 2x^2 - 11x + 12$. Where are the turning points?

6. ## Re: 14th Degree Polynomial Help!

I was told from another person, that there are turning points at around

x = 4.344, x = 0.290, x = -2.492

Its close, but exact. Its somewhere around there.

7. ## Re: 14th Degree Polynomial Help!

Those are 3 of the critical values, the same which I gave many posts ago, only to a greater degree of accuracy.

8. ## Re: 14th Degree Polynomial Help!

MarkFL2

7x^(3)-15x^(2)-72x+22

Thanks

9. ## Re: 14th Degree Polynomial Help!

I have computed approximations for the 3 roots of the cubic polynomial using Newton's method to 12 digits, given you a link to an article about how the method works, given you a link to an article about how to obtain the exact value of the roots. I'm happy with the approximations...I'm not going to use the cubic formula...it is messy and time consuming, and not worth the effort, in my opinion. Substituting the huge cumbersome values into the original function would not be fun either.

So, take the roots of the derivative of odd multiplicity, which have all been found, and evaluate the original function at these roots. These are your turning points.

MarkFL2

11. ## Re: 14th Degree Polynomial Help!

7x^(3)-15x^(2)-72x+22

If not, can anyone tell me how or what would help solve the problem.

12. ## Re: 14th Degree Polynomial Help!

That is called a polynomial!

13. ## Re: 14th Degree Polynomial Help!

OK, whatever. But can you solve it?

14. ## Re: 14th Degree Polynomial Help!

Are you not satisfied with the approximations I gave using Newton's method?

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