Here's the question you clicked on:
johnnyalln
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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
so take \[\frac{d}{dx}\left(-x^2+240x-14400\right)=0\]
solving for x will get you the answer.
Yes totally makes sense now! Thank you!