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Math Help - decreasing function

  1. #1
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    decreasing function

    Find all open intervals on which the function f(x) = \frac {x} {x^2 + x - 2} is decreasing.
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  2. #2
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    f(x) = \frac {x} {x^2+x-2}= \frac {x} {(x+2)(x-1)}

     <br />
1(x^2+x-2)-(2x+1)(x)<br />
    <br />
x^2+x-2-2x^2-x=-x^2-2

    f(prime)(x)= \frac {-(x^2+2)}[\math] {((x+2)(x-1))^2<br />
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  3. #3
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    Quote Originally Posted by Samantha View Post
    Find all open intervals on which the function f(x) = \frac {x} {x^2 + x - 2} is decreasing.
    f^{\prime}(x) = \frac{1 \cdot (x^2 + x - 2) - x \cdot (2x + 1)}{(x^2 + x - 2)^2}

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

    When is this negative? (Hint: The denominator is always positive, since it is squared.)

    -Dan
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  4. #4
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    So it's always decreasing?
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  5. #5
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    Quote Originally Posted by Samantha View Post
    So it's always decreasing?
    It looks like it.

    -Dan
    Attached Thumbnails Attached Thumbnails decreasing function-decreasing.jpg  
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  6. #6
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    so it's (-infinity, -2), (-2,1) and (1, infinity)?
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Samantha View Post
    so it's (-infinity, -2), (-2,1) and (1, infinity)?
    Yup. (You are more exact than I was going to be. I probably wouldn't have removed the points that are outside the domain, and you were right to do so. I would've lost points on this problem. )

    -Dan
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