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Math Help - Help with graph of derivative?

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    Help with graph of derivative?

    For this question: Help with graph of derivative?-capture2.jpgHelp with graph of derivative?-capture3.jpg I have five graph options, and I tried to test each quadrant and I got the closest to the first graph but I'm not sure if it's right. Is Graph I right? If not what could I have messed up on?
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    MHF Contributor ebaines's Avatar
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    Re: Help with graph of derivative?

    Consider that y' is the slop of the function, and if y'=x^2y then the slope = 0 along both the x-axis and y-axis. Graph 1 doesn't fit that criteria. Also as x gets bigger and/or as y gets bigger the slope becomes larger magnitude - always positive for y>0 and always negatiove for y<0. So now, take another look at the 5 graphs and see which one fits the bill.
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    Re: Help with graph of derivative?

    Quote Originally Posted by ebaines View Post
    Consider that y' is the slop of the function, and if y'=x^2y then the slope = 0 along both the x-axis and y-axis. Graph 1 doesn't fit that criteria. Also as x gets bigger and/or as y gets bigger the slope becomes larger magnitude - always positive for y>0 and always negatiove for y<0. So now, take another look at the 5 graphs and see which one fits the bill.
    Oh! I think graph II would work then?
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    MHF Contributor ebaines's Avatar
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    Re: Help with graph of derivative?

    Quote Originally Posted by canyouhelp View Post
    Oh! I think graph II would work then?
    Well, graph II does meet the first two criteria - that the slope is zero along the x- and y-axes and the magnitude of the slope gets bigger with increasing values of x and y. But does it meet the other criteria - is the slope always positive for y>0 and always negative for y<0?
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    Re: Help with graph of derivative?

    Quote Originally Posted by ebaines View Post
    Well, graph II does meet the first two criteria - that the slope is zero along the x- and y-axes and the magnitude of the slope gets bigger with increasing values of x and y. But does it meet the other criteria - is the slope always positive for y>0 and always negative for y<0?
    I think Graph IV works then?
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