
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 24th, 2008, 12:45 AM  #1 
Newbie Joined: Nov 2008 Posts: 16 Thanks: 0  critical points of (24x^2)/(1+x^2)^2
how could i find the critical points of (24x^2)/(1+x^2)^2 i use the quadratic formula and i got +or 1i. does that mean there are no critical points?

November 24th, 2008, 02:39 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond  Re: critical points of (24x^2)/(1+x^2)^2
Since the numerator and denominator are polynomials and the denominator is never equal to 0 the function is continuous, so no critical points there. Critical points also occur where the derivative is equal to zero. One critical point is x = 0. To find the others use 8x^3  16x = 0 and solve for x. 
November 24th, 2008, 03:48 AM  #3 
Newbie Joined: Nov 2008 Posts: 16 Thanks: 0  Re: critical points of (24x^2)/(1+x^2)^2
how do you know 0 is a critical value?

November 24th, 2008, 04:24 AM  #4 
Member Joined: Feb 2008 Posts: 44 Thanks: 0  Re: critical points of (24x^2)/(1+x^2)^2
The derivative of this function will tell you the slope of the function for any given point right? If the derivative of the function is equal to zero, then the function itself must have zero slope, which means that the function has a maximum or minimum at that point (what you call a critical value). Now, because the derivative is a rational function, we need to solve the numerator for 0 (the only way for a fraction to equal zero is if the numerator is equal to zero). (the numerator) factors to Set each factor equal to zero and solve. 

Tags 
24x2 or 1, critical, points, x22 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Critical Points  mathkid  Calculus  1  November 11th, 2012 06:34 PM 
critical points of a function  dean  Calculus  6  September 16th, 2012 07:41 PM 
Critical points and min/max again.  Timk  Calculus  3  November 29th, 2011 10:59 AM 
critical points  summerset353  Calculus  1  March 5th, 2010 01:50 AM 
Critical points  SSmokinCamaro  Calculus  2  April 3rd, 2009 07:04 PM 