What are the critical points of a given function and how can they be solved?

Click For Summary

Homework Help Overview

The discussion revolves around finding the critical points of a given function, specifically a rational function involving a polynomial in the numerator and an exponential term in the denominator. Participants are exploring the challenges associated with solving the first derivative, which is a fifth-degree polynomial.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to solve the first derivative of the function, which is a complex polynomial. There are questions about the correctness of the derivative and the necessity of showing the original function. Some participants express confusion regarding the relevance of factoring the denominator and its impact on finding critical points.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to approach the problem. There is an acknowledgment of the difficulty in factoring the polynomial in the numerator, and some participants are questioning the assumptions about the relevance of the denominator in determining critical points.

Contextual Notes

Participants note that the problem must be solved without the use of a graphing calculator, which adds to the complexity of the discussion. There is also a mention of the necessity to confirm the correctness of the derivative before proceeding.

Allasolid
Messages
4
Reaction score
0

Homework Statement


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

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 . Well more specifically solving the 5th degree polynomial. It needs to be solved without using a graphing calculator.
 
Last edited by a moderator:
Physics news on Phys.org
Please write out the function/polynomial.

Use Latex or text with [ /sup] tags as appropriate. Remove the space between [ /sup when using the superscript tag.
 
Oh here's the derivative i need to solve -ex(3x5+x4-34x3+55x2+169x-216)/(x2-9)2
 
Allasolid said:
Oh here's the derivative i need to solve -ex(3x5+x4-34x3+55x2+169x-216)/(x2-9)2

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

RGV
 
Good point. Sorry I am new to this.

The function is (3x3+4x2-7x+17)/(ex(x2-9))
 
Allasolid said:
Good point. Sorry I'm new to this.

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

Allasolid said:
Oh here's the derivative i need to solve -ex(3x5+x4-34x3+55x2+169x-216)/(x2-9)2
That derivative is correct.

Unfortunately, the polynomial in the numerator does not appear to factor easily. The denominator is factorable.
 
Ohhhhh so i now have (x+3)(x-3)(x+3)(x-3) in the denominator.. :/ sorry i don't see how that's suppose to help.
 
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.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
1K
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 6 ·
Replies
6
Views
1K
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
18
Views
3K
Replies
3
Views
9K