Posted by Confused on Tuesday, November 3, 2009 at 9:52am.
Something is not right about your equation.
The way it is, it would be a parabola opening upwards, and of course it would not have a maximum, but rather a minimum value of N
Are you sure the first term wasn't -t^2 ?
I assume you don't know calculus, so you will have to use the "completing the square" technique (or graphing) to find the t value for which N is greatest.
N = t^2 + 12t + 54
= t^2 + 12t + 36 + 18
= (t+6)^2 + 18
That is SMALLEST when t = -6. I assume you are only interested in t>0. There is no maximum. Are you sure you didn't mean to write
N = t^2 - 12t + 54 ?
Sorry, Yes the correct equation is
-t^2 + 12t + 54
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