5.2 - MATH
1081
 Monday,
February
28
 


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Unformatted text preview: MATH
1081
 Monday,
February
28
 
 Chapter
5
–
Section
2
 
 RELATIVE
EXTREMA
 
 Homework
#7
(due
3/7)
 Section
5.2
#30,
36,
46,
56
 
 
 
 
 
 
 
 
 Section
5.3
#30,
44,
52,
78,
82,
94
 
 Clicker
Check­in:

Choose
any
letter
to
check
in
now.
 Last
time,
we
used
the
sign
of
the
first
derivative
of
a
function
 to
determine
on
which
intervals
the
function
was
increasing
 and
on
which
intervals
the
function
was
decreasing.
 
 To
summarize,
on
intervals
where
 f ' ( x ) > 0 
the
function
 f ( x ) 
 is
increasing
(the
graph
goes
upward
from
left
to
right)
and
on
 intervals
where
 f ' ( x ) < 0 
the
function
 f ( x ) 
is
decreasing
(the
 graph
goes
downward
from
left
to
right).
 
 We
continue
that
discussion
today.

So
really,
there
is
nothing
 new
in
the
way
of
techniques
covered
in
this
section.

There
are
 just
some
new
vocabulary
and
formalization
of
some
ideas.
 Now,
suppose
that
we
have
the
following
results
from
the
 analysis
of
the
sign
of
 f ' ( x ) .
 
 
 What
can
we
say
about
the
value
 f ( −3) ?
 What
can
we
say
about
the
value
 f (1) ?
 
 
 
 
 For
example,
consider
the
graph
of
the
function
 f ( x ) 
here.
 
 
 As
usual,
determining
relative
extrema
by
looking
at
a
graph
of
 the
function
is
fairly
simple.
 
 How
do
we
approach
this
question
of
finding
extrema
when
 given
only
the
algebraic
description?
 
 We
use
the
sign
of
the
derivative
to
tell
us
if
the
direction
of
the
 graph
changes
at
the
critical
number.

If
the
direction
does
 change,
then
we
have
a
relative
extrema.

If
it
does
not,
then
we
 do
not
have
an
extrema.
 
 
 Recall
that
we
defined
critical
numbers
as
points
in
the
domain
 of
 f .

The
direction
of
the
graph
can
change
at
breaks
in
the
 domain
too,
but
those
cannot
be
extrema,
as
the
function
 doesn’t
have
a
value
there.
 
 Example:

Determine
the
location
and
the
value
of
all
relative

 
extrema
(if
any)
for
the
function.
 
 1.

 f ( x ) = −2 x 2 + 8 x + 5 
 
 
 
 2.

 g ( x ) = x 3 − 2 
 
 
 
 1 2 3.

 G ( x ) = x + 2 
 x Example:
Determine
the
location
and
the
value
of
all
relative

 

 
 
 extrema
(if
any)
for
the
function.
 
 1.

 h ( x ) = x1/ 3 
 
 
 
 
 
 2.

 H ( x ) = x 2 / 3 
 Clicker
Check­out:

Choose
any
letter
to
check
out
now.
 
 
 Next
time
–
Section
5.3
 ...
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This note was uploaded on 05/01/2011 for the course MATH 1081 taught by Professor Johanson during the Spring '08 term at Colorado.

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