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

max{nte^{-nt}: t in [0,1]} = ?

2. Relevant equations

3. The attempt at a solution

if f(t) = nte^{-nt}

f '(t)= ne^{-nt}- te^{-nt}

= e^{-nt}(n-t)

set equal to zero to get critical points:

0 = = e^{-nt}(n-t) => two critical points: t1 = n and t2 = -1/n;

plugging the cp's back into the original equation, we get

f(t1) = n^{2}/e^{n2}, which converges to 0 as n-> infy

f(t2) = -e which converges to -e for all n.

What am I doing wrong?

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# Homework Help: Max of cont. fxn

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