Feb 27 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
Relative Extrema
A point c is a
relative (or local) maximum
for f if there are values a < c < b so that
f(c)
≥
f(x) for all a
≤
x
≤
b.
25
20
15
10
5
0
5
10
15
3
2
1
0
1
2
3
4
5
Critical numbers (p.273)
A
necessary
condition for a point to be a relative or
local maximum or minimum is that f
′
(x
0
) = 0.
These points are called
critical values
.
8
6
4
2
0
2
4
6
8
2
1.5
1
0.5
0
0.5
1
1.5
2
Problem
Find the xvalue of all points where the
function f(x) = x
4
 18x
2
has a local
extremum.
f(x) = x
4
 18x
2
3
2
'( )
4
36
4 (
9)
4 (
3)(
3)
critical points
3,0,3
f
x
x
x
x x
x x
x
=
−
=
−
=
−
+
−
3
0
3
x+3
—

+
+
+
x
—
—

+
+
x3
—
—
—

+
f’
—
+
—
+
f(x) = x
4
 18x
2
100
50
0
50
100
150
200
6
3
0
3
6
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