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Idealist

  • 3 years ago

Find all open intervals on which f(x)=x/(x^2+x-2) is decreasing. I found that f'(x)=-(x^2+2)/(x^2+x-2)^2 but what do I do after that?

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  1. frx
    • 3 years ago
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    So when a function is decreasing it's derivitive is negative, so you simply set the inequality \[\frac{ -(x ^{2}+2) }{ (x ^{2}+x-2)^{2} } < 0\]

  2. Idealist
    • 3 years ago
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    So is the answer (negative infinity, -2)U(-2, 1)U(1, infinity)?

  3. frx
    • 3 years ago
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    Correct

  4. Idealist
    • 3 years ago
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    Thank you.

  5. frx
    • 3 years ago
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    np

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