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Math Help - when the f(x) positive, negative, or zero

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    when the f(x) positive, negative, or zero

    How to determine, when the first and second derivatives of f(x) is positive, negative, or zero.
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    Quote Originally Posted by venikUSA View Post
    How to determine, when the first and second derivatives of f(x) is positive, negative, or zero.

    When f(x) is increasing, f ' (x) will be positive

    When f(x) is decreasing, f ' (x) will be negative

    When f(x) is concave down, f '' (x) will be negative

    When f(x) is concave up, f '' (x) will be positive

    When f(x) changed from increasing to decreasing (or vice versa) f ' (x) = 0

    When f(x) changes in concavity, f '' (x)= 0

    If it helps you, graph all three on the same graph and look at what changes.
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