March 1 Lecture
HWK #5 due R 3/8 or F 3/9
5.3: 36, 42, 50, 68
6.1: 14, 16, 43
6.2: 9, 18, 26
Spring Break March 1725
Prelim 2: Thursday March 29
Prelim 2 changes
• Solutions will be available on the web after
the exam is over.
• No questions will be answered during the
exam
• All four TAs will be present
March 1 Lecture
A necessary condition to be an extremum
(minumum or maximum) is f
′
(c)=0
Second derivative test
f
′′
(c) > 0 convex, minimum
f
′′
(c) < 0 concave, maximum
Problem
2
Where does the function
()
1
achieve its maximum for t > 0?
t
ft
t
=
+
Maximize
f(t) = t / (1+t
2
)
22
2
2
24
2
4
1(1
)
(2 )
1
'( )
(1
)
)
'(1)
0
2(1
)
) 2(1
)
(2)
"( )
)
2(2)
"(1)
0
maximum
2
tt
t
t
f
t
t
f
+−
−
==
++
=
−+
−
−
⋅
+
=
+
−
=<
Problem
The energy E expended by a bird looking for food,
depends on the amount of time F spent foraging
for food. Find the time F that minimizes E if
2
2
0.25
EF
F
=+
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View Full DocumentMinimize E = 0.25F + 2/F
2
3
31
/
3
4
1
'( )
4
4
16
(16)
''( )
12
0
minimum
EF
F
FF
F
−
−
=−
==
=>
Optimal can design Example 4 in 6.2.
In manufacturing a cylindrical can the top
and bottom costs 1.5 times as much as
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 Spring '07
 DURRETT
 Calculus, Optimization, Fermat's theorem, Spring Break

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