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Math Help - function local extrema etc

  1. #1
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    function local extrema etc

    f(x)= e^10x/ 1+ e^10x graph this function when -5<= x <= 5.
    find the notable features of this graph, including any local extrema points of inflection and asymptotes.

    then sketch a plausible graph for e^10000x / 1 + e^10000x.

    well are both graphs not just a horizontal line at 1?
    so what would the local extrema and points of inflection be?
    i have to write out the answer to the problem. So it would be something like when i graphed this problem it was pretty much a straight line so.....

    am i correct in my thinking or am i bugging out?
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  2. #2
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    \frac{e^{ax}}{1+ e^{ax}}, for large a, will be very close to 0 for negative x and very close to 1 for positive x. Close to x= 0, the function rises very sharply from 0 to 1- how sharply depending on how large a is.
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