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Math Help - Increasing/decreasing intervals of a function

  1. #1
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    Increasing/decreasing intervals of a function

    1 ) Let g(a,b) R and let x0 (a,b).
    Match the two lists.

    A(x0,g(x0)) is a critical point Bg is decreasing on (a,b) Cg is increasing on (a,b) Dx0 is a critical number

    C g(x) > 0 for all x (a,b).
    B g(x) < 0 for all x (a,b).
    A For any x1,x2 (a,b),

    x1 < x2 g(x1) < g(x2).

    D x0 is a critical number.
    D g(x0)=0
    D g(x0) does not exist.

    2.) For f(x) = x6 /7 -x13 /7 find the critical numbers and open intervals where the function is increasing and decreasing.

    Solution:
    Since f(x)= ____________

    ,we see that f(x)=0 if x= __________ and that f( __________ ) does not exist.
    Therefore, the critical numbers are __________ and __________ .

    is increasing on an interval if f(x) > for each x on that interval. Therefore the given function is increasing on the interval ( __________ , __________ ).
    f is decreasing on an interval if f(x) < for each x on that interval. Therefore the given function is decreasing on (- , __________ )( __________ ,).


    The text in red is the answers i got..but there is something wrong with it...can someone help me...and there are two questions where i am completely clueless ...can anyone help! appreciate it
    Last edited by lemontea; July 14th 2008 at 09:19 PM.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by lemontea View Post
    1 ) Let g(a,b) R and let x0 (a,b).
    Match the two lists.

    A(x0,g(x0)) is a critical point Bg is decreasing on (a,b) Cg is increasing on (a,b) Dx0 is a critical number

    C g(x) > 0 for all x (a,b). yes..
    B g(x) < 0 for all x (a,b). yes..
    A For any x1,x2 (a,b),

    x1 < x2 g(x1) < g(x2). answer is C. try to graph by giving some examples..

    D x0 is a critical number. i say A. (of course, one would choose D but see, D is just a re-statement of the question.)
    D g(x0)=0 yes..
    D g(x0) does not exist. yes..

    2.) For f(x) = x6 /7 -x13 /7 find the critical numbers and open intervals where the function is increasing and decreasing.

    Solution:
    Since f(x)= ____________

    ,we see that f(x)=0 if x= __________ and that f( __________ ) does not exist.
    Therefore, the critical numbers are __________ and __________ .

    is increasing on an interval if f(x) > for each x on that interval. Therefore the given function is increasing on the interval ( __________ , __________ ).
    f is decreasing on an interval if f(x) < for each x on that interval. Therefore the given function is decreasing on (- , __________ )( __________ ,).


    The text in red is the answers i got..but there is something wrong with it...can someone help me...and there are two questions where i am completely clueless ...can anyone help! appreciate it
    i don't understand the thing in orange. is it f(x) = \frac{x_6}{7}-\frac{x_{13}}{7}?
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