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Math Help - Help with graph of first and second derivatives?

  1. #1
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    Help with graph of first and second derivatives?

    I have this question: Help with graph of first and second derivatives?-capture2.jpgnow I think the answer is either B or E because I remember little bits and pieces of the rules for the graph of the derivative and second derivative, but I can't remember exactly so I'm not sure. Which one would it be and why? Or am I just completely off? Thanks!
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Help with graph of first and second derivatives?

    First you want the value of g to be greater than g'. Remember that g' is the slope. At point E note that the value of g is as negative as it can get, and the slope is zero, so g < g' and this can't be the right answer. Hint: find a point where g is positive, g' is 0 and g'' is negative. To determine whether g'' is positive or negative consider how the slope is changing nearby. For example at C the slope looks pretty constant - therefore g'' is close to 0, and at E the slope is quickly changing from negative to psoitive, so g'' is positive. Hope this helps!
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    Re: Help with graph of first and second derivatives?

    Quote Originally Posted by ebaines View Post
    First you want the value of g to be greater than g'. Remember that g' is the slope. At point E note that the value of g is as negative as it can get, and the slope is zero, so g < g' and this can't be the right answer. Hint: find a point where g is positive, g' is 0 and g'' is negative. To determine whether g'' is positive or negative consider how the slope is changing nearby. For example at C the slope looks pretty constant - therefore g'' is close to 0, and at E the slope is quickly changing from negative to psoitive, so g'' is positive. Hope this helps!
    Thank you, would point B work then? In B g is positive, the slope, g', is 0 and wouldn't g" be negative?
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    MHF Contributor ebaines's Avatar
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    Re: Help with graph of first and second derivatives?

    Yes, correct!
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    Re: Help with graph of first and second derivatives?

    Quote Originally Posted by ebaines View Post
    Yes, correct!
    Thank you!
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