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December 3rd, 2017, 03:49 PM   #1
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derivative of the function

hi guys,
I am trying to match the function with its derivative on the graph.
Any idea which could be the derivative of the blue line and why?

thanks a lot.
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 December 3rd, 2017, 03:56 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond The derivative is zero where the function has a local min/max. The steeper the curve is, the greater in value the derivative is - with negative "steepnes" having a greater negative value and positive steepness having a greater positive value. In short, the greater the absolute value of the derivative the more steeply the curve is inclined. Does that help?
 December 3rd, 2017, 04:34 PM #3 Senior Member   Joined: Apr 2017 From: New York Posts: 164 Thanks: 6 so which one is the answer below, please?
 December 3rd, 2017, 05:04 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond It's hard to tell without knowing where the x-axis is. Besides, I was hoping you'd be able to answer that. What do you think?
December 3rd, 2017, 05:19 PM   #5
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I eliminated number 1 and 2 on my mind but this is a sensitive question that I have only one chance to input. not a second chance is given so wanted to make sure 100%.

According to your explanations it seems 3. but again need to make sure before inputting.
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 December 3rd, 2017, 05:37 PM #6 Math Team     Joined: Jul 2011 From: Texas Posts: 3,038 Thanks: 1622 Not 3 ... note the slope of the original function is negative, positive, and negative from left to right. Also note the slope is positive at x = 0 Thanks from greg1313
 December 3rd, 2017, 06:02 PM #7 Senior Member   Joined: Sep 2016 From: USA Posts: 670 Thanks: 440 Math Focus: Dynamical systems, analytic function theory, numerics It is #4. Now, with that known, can you figure out why? What does the derivative tell you about the function? Hint: Look at the 2nd derivative.
December 3rd, 2017, 11:04 PM   #8
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Quote:
 Originally Posted by greg1313 The derivative is zero where the function has a local min/max...
Provided that f is smooth and continuous around that point.

 December 4th, 2017, 11:15 AM #9 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 One of the first things you should have seen from the original graph (of the derivative) is that the derivative is positive from some negative x value to some positive x value. There must be an interval from a negative x to a positive x where the graph is positive. Only one of the four graphs has that property.
 December 4th, 2017, 02:24 PM #10 Global Moderator   Joined: Dec 2006 Posts: 21,035 Thanks: 2272 As the curve crosses the vertical line, its slope (derivative) changes from increasing to decreasing, so it has a local maximum at the point where it crosses the vertical line. Only the "last" graph has that property.

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