# Homework Help: Finding Critical Points

1. Nov 28, 2011

### Allasolid

1. The problem statement, all variables and given/known data
I need to find the critical points of this functionhttp://www4a.wolframalpha.com/Calculate/MSP/MSP84719i6a1iabg11598d000049hhhie62iif1c81?MSPStoreType=image/gif&s=16&w=140&h=46 [Broken]

3. The attempt at a solution
I'm having trouble solving the first derivative, which is http://www4a.wolframalpha.com/Calculate/MSP/MSP12919i6a079bg6ed96c00003ed60iee4d866bb3?MSPStoreType=image/gif&s=39&w=493&h=48 [Broken]. Well more specifically solving the 5th degree polynomial. It needs to be solved without using a graphing calculator.

Last edited by a moderator: May 5, 2017
2. Nov 28, 2011

### Astronuc

Staff Emeritus

Use Latex or text with [ /sup] tags as appropriate. Remove the space between [ /sup when using the superscript tag.

3. Nov 28, 2011

### Allasolid

Oh heres the derivative i need to solve -ex(3x5+x4-34x3+55x2+169x-216)/(x2-9)2

4. Nov 28, 2011

### Ray Vickson

You should show the function itself as well. How do we know your derivative is correct?

RGV

5. Nov 28, 2011

### Allasolid

Good point. Sorry im new to this.

The function is (3x3+4x2-7x+17)/(ex(x2-9))

6. Nov 28, 2011

### SammyS

Staff Emeritus
That derivative is correct.

Unfortunately, the polynomial in the numerator does not appear to factor easily. The denominator is factorable.

7. Nov 28, 2011

### Allasolid

Ohhhhh so i now have (x+3)(x-3)(x+3)(x-3) in the denominator.. :/ sorry i dont see how thats suppose to help.

8. Nov 28, 2011

### HallsofIvy

Unless it cancels things in the numerator (and you can check that by seeing if x= 3 or x= 3 will make the numerator equal to 0), factoring the denominator is irrelevant. A fraction, a/b, is equal to 0 only if a= 0. You don't need to worry about the denominator. It is also true that $e^x$ is never 0 so it all reduces to solving $3x^5+ x^4- 34x^3+ 55x^2+ 169x- 216= 0$.