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March 29, 2017

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Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=9x^4-3x^2+5x-1;[0,1]

  • Use the intermediate value - ,

    There are a number of ways to do this, lets go to the idiot's guide to Math...

    f(0)=-1
    f(1)=9-3+5-1=10

    so how can one get to 10 from -1 by not crossing the y=0 axis?

  • Use the intermediate value - ,

    Not sure that is why I asked :)

  • Use the intermediate value - ,

    The IVT is dependent on the fact that f(x) is continuous. That is, f(x) cannot get from -1 to 10 without being 0 somewhere on the way.

    If f is not continuous, then there might be a hole at f=0, so there would be no guarantee that f(c)=0 for some 0<c<1.

  • Use the intermediate value - ,

    Reread the intermediate value theorem, it concludes that one can't get to 10 from -1 with a continuous function without passing the y=0 axis. Often, the mean value, and intermediate value theorem are written in math texts by lawyer want-to-be types, so complex, it loses its meaning.

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