anonymous
  • anonymous
m
Mathematics
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anonymous
  • anonymous
m
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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