# Homework Help: Local Max &amp; Min problem

1. Apr 7, 2008

### prophet05

[SOLVED] Local Max &amp; Min problem

I'm having a real tough time finishing this problem. I have to find the local maxima and minima points for g(x).

g(x) = 1 + 4x - 10x^2 + x^4

(dy/dx) = 4 - 20x + 4x^3

I've been trying to factor it to get the max and min points, but I find it impossible to simplify. I've tried factoring and just can't seem to find a way. And I can't use quadratic formula since it's to the 3rd degree, right?

2. Apr 7, 2008

### Snazzy

The first thing I thought of was Newton's method because I'm not great when it comes to solving the zeros for that with pure algebra.

3. Apr 7, 2008

### Feldoh

Well here's the cubic formula:

For a cubic of the form ax^3+bx^2+cx+d

The roots are: 0.2016396757234, 2.12841906384458, -2.33005873956798

So Newton's method seems like that way to go.

4. Apr 8, 2008

### prophet05

Yea, the cubic formula is out, I am not going to mesmerize that. I'll try and read up on Newton's method.

5. Apr 8, 2008

### Snazzy

Newton's method is a powerful tool for finding zeros. Take a guess, x_n, at what x-value the zero could be at:

Then $$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$$

Then take the value of $$x_{n+1}$$ that you got and do the above calculation over and over again (around four or five times) until the number that you obtain settles down.

The only problem is that it doesn't tell you how many zeros the function has.

6. Apr 8, 2008

### HallsofIvy

"Mesmerize" it? Now why didn't I think of that! I'll just hynotize formulas into doing my bidding!

7. Apr 8, 2008

### Feldoh

It's all part of the plan for world domination mwhahahaha!11!oneone!1!1

8. Apr 8, 2008

### BrendanH

I don't usually jump on the bandwagon of a string of jokes, but that 'mwahahaha!11!oneone... had me rofl-ing!!!

9. Apr 9, 2008

### prophet05

Haha. Thanks for all the help. Turns out the professor wanted us to solve it with calculator. Mesmerize would have been a better way to go. =P

$$g(x) = 1 + 4x - 10x^2 + x^4$$
$$(dy/dx) = 4 - 20x + 4x^3$$

Last edited: Apr 9, 2008