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March 27 Lecture
HWK #7 due April 5/6
7.4: 5, 12, 13, 16, 27
8.2: 2, 14
8.4: 2, 14, 19, 24
Problem
(a) Find all the critical points,
(b) Use the second derivative test to
determine if they are local max or min
Find the open intervals on which the function
is (c) increasing, (d) convex
53
54
xx
x
−+
f(x) = x
5
/5 – 5x
3
/3 + 4x
42
2
2
32
'( )
5
4
(
1)(
4)
(
2)(
2)
''( )
4
10 =4 (
2.5)
critical points
2, 1,1, 2
"
32
20,
4
10,
4
32
20
max
min
max
min
convex when
2.5
or

2.5
fx x
x
x
x
x
x
fx
x
x x
x
f
x
=−
+
=
−
−
=+
+
−
−
−
−−
+
− +
−
−
↑↓
><
0
x
<
f(x) = x
5
/5 – 5x
3
/3 + 4x
crit. pts. 2,1,1,2
(2.5)
½
= 1.58
5
4
3
2
1
0
1
2
3
4
5
2.5
2
1.5
1
0.5
0
0.5
1
1.5
2
2.5
Max and min don’t always alternate
42 2
3
() 3
5
15
15
15
(
1)
60
30
critical points
1,0,1
''
30,0,30
max, ?, min
increasing
1,
1
decreasing
1
x
x
x
x
x
x
x
f
x
=−=
+
−
−
<−
>
−<<
f(x) = 3x
5
–5x
3
6
4
2
0
2
4
6
1.5
1
0.5
0
0.5
1
1.5
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View Full Document MaxMin word problem
The San Diego zoo is going
to build an enclosure for
birds. It will have height h
and the base will be an r
by r square. Suppose
they have 300 square
feet of fencing. What is
the largest volume they
can enclose?
x
rr
h
Max r
2
h
when
r
2
+ 4rh = 300
23
2
2
300
300
44
300
3
'0
4
when
10,
200 / 40
5
''
6 / 4
0
so this is a maximum
r
hV
r
h
r
r
V
rh
Vr
−−
==
=
−
=
=−
<
Name that substitution
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 DURRETT
 Calculus, Critical Point, Derivative

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