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johnnyalln

  • 2 years ago

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  1. richyw
    • 2 years ago
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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.

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

  3. richyw
    • 2 years ago
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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

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

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

  6. richyw
    • 2 years ago
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    solving for x will get you the answer.

  7. richyw
    • 2 years ago
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    make sense?

  8. johnnyalln
    • 2 years ago
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    Yes totally makes sense now! Thank you!

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