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: 7,540 Thanks: 920 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: 462 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: 462 Math Focus: Calculus/ODEs  Re: 1st derivative test
You gave different intervals...I just wanted to demonstrate the method I was taught to use.


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