(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the absolute maximum for f(t) = -t^3 + 3t^2 + 400t + 5000, t is between 6 and 20.

2. Relevant equations

f'(t) = -3t^2 + 6t + 400

3. The attempt at a solution

I know how to find this - when the function can be perfectly factored. Yet some problems occur here.

f'(t) = -3t^2 + 6t + 400

I normally factor to find minimum, but 400 divided by -3 = -133.33333~, meaning the answer will be approximate (technically) if I do that... Now the second derivative will come to something really easy, 6t+6... Can absolute maximums be found with the second derivative? If not, how can it be found here?

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# Homework Help: Find the absolute maximum for f(t) = -t^3 + 3t^2 + 400t + 5000

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