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May 3rd, 2012, 08:31 AM  #1 
Newbie Joined: May 2012 Posts: 12 Thanks: 0  Graphs of Functions and their derivatives
I'm having alot of trouble with this assignment could you possibly help explain what exactly im looking for and how i would go about answering these graphs? pelase and thanks!

May 3rd, 2012, 09:18 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Graphs of Functions and their derivatives
Let's begin with problem 1 part a. Using the given information, where is the function decreasing? And how do you know? 
May 3rd, 2012, 09:24 AM  #3 
Newbie Joined: May 2012 Posts: 12 Thanks: 0  Re: Graphs of Functions and their derivatives
so far... we only ahve the info on the derivative correct? and looking at that im not sure what to think except that when the derivative is less than 3 the graph is lower than 0.. and the graph is above 0 when the graph is greater than 3 sorry kinda just skipped into this 
May 3rd, 2012, 09:32 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Graphs of Functions and their derivatives
Yes, the only information given is concerning the derivative. The derivative gives you information about how the function associated with it is changing with respect to the independent variable. A function is increasing where its derivative is positive and is decreasing where its derivative is negative, and is stationary where the derivative is zero. So, using the information given, where is the function decreasing? 
May 3rd, 2012, 11:31 AM  #5 
Newbie Joined: May 2012 Posts: 12 Thanks: 0  Re: Graphs of Functions and their derivatives
so that means since the function is decreasing when the derivative is negative taht would mean when x < 3 ? and its increasing when x > 3? 
May 3rd, 2012, 11:59 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Graphs of Functions and their derivatives
Yes, exactly. So which given graph matches that description?

May 3rd, 2012, 12:06 PM  #7 
Newbie Joined: May 2012 Posts: 12 Thanks: 0  Re: Graphs of Functions and their derivatives
the first one?

May 3rd, 2012, 12:07 PM  #8 
Newbie Joined: May 2012 Posts: 12 Thanks: 0  Re: Graphs of Functions and their derivatives
the first one correct?*

May 3rd, 2012, 12:15 PM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Graphs of Functions and their derivatives
Yes, the first graph matches the given description. Without use the graph, how then would you describe the behavior of the function using the information given? You've already determined the function is decreasing on (?,3) and increasing on (3,?), so given that , what does the first derivative test for relative extrema tell us? Do we have enough information to discuss concavity and points of inflection? 
May 3rd, 2012, 12:27 PM  #10 
Newbie Joined: May 2012 Posts: 12 Thanks: 0  Re: Graphs of Functions and their derivatives
that the graph is decreasing before 3 and increasing after 3 and has a relative minimum at (3,0)


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