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Math Help - increasing function

  1. #1
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    increasing function

    find all open intervals on which the function f(x)= x/ x^2 + x -2 is decreasing
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  2. #2
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    Quote Originally Posted by gracy View Post
    find all open intervals on which the function f(x)= x/ x^2 + x -2 is decreasing
    Let:

    f(x)=\frac{x}{x^2+2-2},

    then:

    f'(x)=-\frac{x^2+2}{(x^2+x-2)^2}

    which is always <0 where it is defined. It is undefined at the roots of x^2+x-2 which are x=-2 and x=1.

    Also f(x) is decreasing where f'(x)<0.

    Therefore f(x) is decreasing on (-\infty,-2),\ (-2,1) and (1,\infty)

    RonL
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