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December 3rd, 2017, 04:49 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, 04:56 PM   #2
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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?
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December 3rd, 2017, 05:34 PM   #3
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so which one is the answer below, please?
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December 3rd, 2017, 06:04 PM   #4
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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?
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December 3rd, 2017, 06:19 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, 06:37 PM   #6
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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
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December 3rd, 2017, 07:02 PM   #7
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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.
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December 4th, 2017, 12:04 AM   #8
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The derivative is zero where the function has a local min/max...
Provided that f is smooth and continuous around that point.
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December 4th, 2017, 12:15 PM   #9
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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.
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December 4th, 2017, 03:24 PM   #10
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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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