October 6th, 2012, 03:30 PM  #1 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  1st derivative test
For the following function, fill in the table to find where the function is increasing or decreasing. y = f(x) = x^(2) + 6x + 10 f ' (x) = 2x + 6 open interval infinity<x<0 0<x<+infinity Test # 2 1 sign of f '(x) increasing increasing conclusion ? ? minimum occurs at ? is it 3 ? Thanks for any and all help 
October 6th, 2012, 05:41 PM  #2  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,806 Thanks: 1045 Math Focus: Elementary mathematics and beyond  Re: 1st derivative test Quote:
2x + 6 = 0 2x = 6 x = 6/2 = 3. Note that f(x) is a parabola, so there is one (global) extremum, a minimum at x = 3, y = 1. Good work.  
October 6th, 2012, 06:29 PM  #3 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: 1st derivative test
Thanks Greg

October 6th, 2012, 06:30 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: 1st derivative test
To determine the intervals on which the function is increasing/decreasing, you first find the critical number(s). For this function this is This gives you the two intervals: i) Test value function decreasing on this interval. ii) Test value function increasing on this interval. So, we can therefore conclude that the function has a relative (in this case a global) minimum at . 
October 6th, 2012, 07:14 PM  #5 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: 1st derivative test
I got it right Mark. Need help on other question finding critical value(s).

October 6th, 2012, 07:22 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: 1st derivative test
You gave different intervals...I just wanted to demonstrate the method I was taught to use.


Tags 
1st, derivative, test 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
First Derivative Test  SamFe  Calculus  1  November 7th, 2013 12:04 PM 
What does this mean: f' does not exist (1e derivative test)  Gerrit  Calculus  13  October 14th, 2013 04:33 AM 
Second Derivative Test  BrianMX34  Calculus  3  November 3rd, 2012 12:05 PM 
Help with graphing second derivative test on Ti84......  RealMadrid  Calculus  1  July 19th, 2012 02:24 PM 
Second Derivative Test  SyNtHeSiS  Algebra  5  May 26th, 2010 04:28 AM 