- #1
Somefantastik
- 230
- 0
Homework Statement
max{nte-nt: t in [0,1]} = ?
Homework Equations
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) = n2/en2, which converges to 0 as n-> infy
f(t2) = -e which converges to -e for all n.
What am I doing wrong?