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Math Help - Open Intervals

  1. #1
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    Open Intervals

    I plugged in the equation -x^4-2x^3+5x+4 into my calculator. I'm looking at the graph, but I can't find the points of inflection.

    The problem is f(x)=-x^4-2x^3+5x+4 and I must find the intervals in which f is concave up (down), Then I have to determine the x-coordinates of all inflection points of f.


    So far I know that one of the concave down intervals is (0,infinity)



    The method I used to get that cannot be used for the others so I'm here to ask for help on how to do this right.
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  2. #2
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    Solving for f''(x)=0 will give you the values of x at which f(x) has points of inflection. Indeed, f''(x)=-12x(x+1)=0 when x=-1,\,0. So you should investigate the behaviour of f(x) in the three separate intervals (-\infty,\,-1),\ (-1,\,0),\ (0,\,\infty).
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  3. #3
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    Thank you, I was missing going to the second derivative. Thanks.
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