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Math Help - Find out all the existing maximum and minimum in the following functions

  1. #1
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    Find out all the existing maximum and minimum in the following functions

    Hi, I am having difficulty solving a few of these maximum/minimum equations and would appreciate any help given!

    f(x)= 1/(x-1), x ∈ R

    and it says, note that R is the set of all real numbers.

    If maybe you could explain to me what the thought process is so solving this, then I could do the rest myself.

    Any help is much appreciated

    Regards

    Kam
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  2. #2
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    a necessary (but not sufficient) condition for f to have a local maximum or minimum at a, is that f'(a) = 0.

    in the case at hand, f'(x) = 1/(x-1)^2, which is never 0. so if f has a maximum or minimum, it must be global.

    if ±infinity doesn't count, f has no minimum. f(x) gets very small as |x| gets large, but it is never 0. it has a horizontal asymptote (the x-axis).

    f(x) is unbounded in any neighborhood of 1, and undefined at 1, it has a vertical asymptote at x = 1.

    if we changed variables, by letting u = x-1, f(u) = 1/u. so the graph of f looks just like the graph of g(x) = 1/x, but "shifted right by 1".
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  3. #3
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    wow, thank you for the explanation, although that was greek to me! is what you have shown me the actual answer or a general explanation of how max/mins work?

    I thought the answer was supposed to be something like x=0 or something like that, i have no idea where you supposed to get f'(a) and u and g(x) from?

    Sorry im trying to understand, iv only been presented with this sort of maths yesterday and i have my assignment in for a couple days time! dont know how they expect us to understand this...

    im really stuck now! :/ could you possibly show me how you would answer the question and then i could understand things better?

    regards

    Kam
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by simagen View Post
    wow, thank you for the explanation, although that was greek to me! is what you have shown me the actual answer or a general explanation of how max/mins work?

    I thought the answer was supposed to be something like x=0 or something like that, i have no idea where you supposed to get f'(a) and u and g(x) from?

    Sorry im trying to understand, iv only been presented with this sort of maths yesterday and i have my assignment in for a couple days time! dont know how they expect us to understand this...

    im really stuck now! :/ could you possibly show me how you would answer the question and then i could understand things better?

    regards

    Kam
    What course is this for?

    CB
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