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Math Help - Absolute min and max help.

  1. #1
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    Absolute min and max help.

    The instructions say sketch graph by hand and use sketch to find absolute and locx and min for values of f.

     f(x)= ln x, 0 < x \leq 2
    The answer is abs max is f(2) = ln 2

    I can see that there is no local max or min (i cheated though and didn't draw the graph, just that f'(x) can't equal to 0)

    But I can see how 2 would be the absolute max because it's the biggest number in the interval, and no absolute min because the function will always try to reach 0 but doesn't reach it.

    But the Extreme value theorem in the book says that
    If F is continous on a closed interval [a,b], then f attains an absolute maximum value of f(c) and an absolute min at f(d) at some number c and d in [a,b]

    doesn't that mean to have absolute max or min, the function has to be on a closed interval?
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  2. #2
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    Quote Originally Posted by dorkymichelle View Post

    But the Extreme value theorem in the book says that
    If F is continous on a closed interval [a,b], then f attains an absolute maximum value of f(c) and an absolute min at f(d) at some number c and d in [a,b]

    doesn't that mean to have absolute max or min, the function has to be on a closed interval?
    Note that:
     x \in [a,b] = a \leq x \leq b
     x \in (a,b] = a < x \leq b
     x \in [a,b) = a \leq x < b
     x \in (a,b) = a <x<b

    So the definition in your book says the max lies within [a,b]. This includes when x = a or b too.
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