12. (a)
The domain is
x
2. (See the solution for 11.(c)).
(b)
f
9
(
x
)
5
h
Section 4.1 Exercises
1.
Maximum at
x
5
b
, minimum at
x
5
c
2
;
The Extreme Value Theorem applies because
f
is
continuous on [
a
,
b
], so both the maximum and minimum
exist.
2.
Maximum at
x
5
c
, minimum at
x
5
b
;
The Extreme Value Theorem applies because
f
is
continuous on [
a
,
b
], so both the maximum and minimum
exist.
3.
Maximum at
x
5
c
, no minimum;
The Extreme Value Theorem does not apply, because the
function is not defined on a closed interval.
4.
No maximum, no minimum;
The Extreme Value Theorem does not apply, because the
function is not continuous or defined on a closed interval.
5.
Maximum at
x
5
c
, minimum at
x
5
a
;
The Extreme Value Theorem does not apply, because the
function is not continuous.
6.
Maximum at
x
5
a
, minimum at
x
5
c
;
The Extreme Value Theorem does not apply since the
function is not continuous.
7.
Local minimum at (
2
1, 0), local maximum at (1, 0)
8.
Minima at (
2
2, 0) and (2, 0), maximum at (0, 2)
9.
Maximum at (0, 5) Note that there is no minimum since the
endpoint (2, 0) is excluded from the graph.
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 Fall '08
 GERMAN
 Calculus, Derivative, maximum

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