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johnnyalln

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  • one year ago
  • one year ago

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  1. richyw
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    first of all this is a quadratic function, so you know that there will be only one max/minimum. Since the \(x^2\) term has a negative coeffeicient you know that it's going to be opening downwards and therefore have one maximum and no minimum.

    • one year ago
  2. johnnyalln
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    got it. I am with you there so far!

    • one year ago
  3. richyw
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    so now that you know this you can simply differentiate the equation, which gives you the slope of the line tangent to the parabola at any point. the slope will be zero at this maximum

    • one year ago
  4. richyw
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    so take \[\frac{d}{dx}\left(-x^2+240x-14400\right)=0\]

    • one year ago
  5. richyw
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    \[-2x+240=0\]

    • one year ago
  6. richyw
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    solving for x will get you the answer.

    • one year ago
  7. richyw
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    make sense?

    • one year ago
  8. johnnyalln
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    Yes totally makes sense now! Thank you!

    • one year ago
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spraguer (Moderator)
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