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johnnyalln Group Title m one year ago one year ago

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1. richyw Group Title

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 Group Title

got it. I am with you there so far!

3. richyw Group Title

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 Group Title

so take $\frac{d}{dx}\left(-x^2+240x-14400\right)=0$

5. richyw Group Title

$-2x+240=0$

6. richyw Group Title

solving for x will get you the answer.

7. richyw Group Title

make sense?

8. johnnyalln Group Title

Yes totally makes sense now! Thank you!