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Math Help - value of a fcn, and its derivatives, translated into english.

  1. #1
    szangomango
    Guest

    Exclamation value of a fcn, and its derivatives, translated into english.

    Hello,
    I am having a really difficult time understanding this. I think my main problem is it is written in english and its confusing the heck out of me.

    I am trying to understand what is happening if the value of f(x) is positive, the value of f '(x) is negative, and the value of f ''(x) is positive.

    If anyone can help me understand this, i would greatly appreciate any input offered.
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Your flag is the USA flag, so you must be in the USA now, or you are from the USA.

    I hope the English language is still okay in the USA.

    Sorry but I have to explain it in English.
    Oh, English is not my native tongue too, so you might understand what I will write.

    -------------------------------------------------------

    If the value of the function, f(x), is positive, it means the function is more than zero. It means also that its graph at that point is above the x-axis.

    If the value of the first derivative, f'(x), is negative, it means the f(x) is decreasing in value at that point.
    Also, it means the graph is going down at that point.
    Also, the slope of the tangent line at that point is negative, or it the tangent line is leaning to the left.

    If the value of the second derivative, f''(x), is positive, it means the concavity of its graph at that point is facing upwards.
    If the value of f(x) is losing at that point, the positive f''(x) means the value of f(x) at that point is recovering from loss, the steepness of the loss is weakening.
    If the f(x) is gaining at that point, it is getting to gain in value a bit faster.
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