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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.
got it. I am with you there so far!
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

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so take \[\frac{d}{dx}\left(-x^2+240x-14400\right)=0\]
\[-2x+240=0\]
solving for x will get you the answer.
make sense?
Yes totally makes sense now! Thank you!

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