6.2 - MATH
1081
 Wednesday,
March
9
 


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Unformatted text preview: MATH
1081
 Wednesday,
March
9
 
 Chapter
6
–
Section
2
 
 APPLICATIONS
OF
EXTREMA
 
 Homework
#8
(due
3/14):
 
 Section
6.1
#14,
22,
24,
56
 
 
 
 
 
 
 
 
 
 Section
6.2
#14,
18,
22,
26
 

 Clicker
Check­in:

Press
any
letter
to
check
in
now.
 Last
time,
we
discussed
how
to
find
the
absolute
extrema
of
a
 function.

In
this
section,
we
use
these
same
techniques
to
solve
 problems
of
optimization,
where
we
are
trying
to
maximize
or
 minimize
some
quantity.
 
 As
noted
in
the
last
section,
when
finding
the
absolute
extrema
 of
a
function,
particular
attention
must
be
paid
to
the
domain
 of
that
function.

In
the
setting
of
the
applications
that
we
will
 see
today,
that
continues
to
be
a
very
important
component
of
 the
solution
to
the
problem.
 
 Example:

Section
6.2
#4:

Find
nonnegative
integers
 x 
and
 y 
 
 
 
so
that
 x + y = 90 
and
 x 2 y 
is
maximized.
 
 Example:

Section
6.2
#12:

A
fence
must
be
built
to
enclose
a

 
 
 
 
rectangular
area
of
20,000
square
feet.

Fencing
 
 
 
 
material
costs
$2.50
per
foot
for
the
two
sides
 
 
 
 
facing
north
and
south,
and
$3.20
per
foot
for
the

 
 
 
 
other
two
sides.

Find
the
cost
of
the
least
expensive
 
 
 
 
fence.
 
 Example:

Section
6.2
#40:

Homing
pigeons
avoid
flying
over

 large
bodies
of
water….

Assume
that
a
pigeon
is
 released
from
a
boat
1
mile
from
the
shore
of
a
lake
 first
flies
to
a
point
P
on
the
shore
and
then
along
 the
straight
edge
of
the
shore
to
its
home
which
is
2
 miles
from
the
point
on
the
shore
closest
to
the
 boat.

If
the
pigeon
needs
4/3
as
much
energy
to
fly
 over
water
as
over
land,
find
the
location
of
the
 point
P
which
minimizes
the
energy
used.
 
 

 Example:

Section
6.1
#57:

A
piece
of
wire
12
feet
long
is
cut

 into
two
pieces.

One
piece
is
bent
into
the
shape
of
 a
circle
and
the
other
piece
is
bent
into
the
shape
of
 a
square.

Where
should
the
cut
be
made
to
make
 the
sum
of
the
areas
maximum?
 Clicker
Check­out:

Choose
any
letter
to
check
out
now.
 
 
 Tomorrow
in
recitation:
Quiz
#4
on
Sections
4.4,
4.5,
5.1,
5.2,
5.3
 
 
 There
are
some
potentially
useful
formulas
for
geometry
in
the
 appendix
of
the
text
(page
A‐1).
 
 Next
time
–
Section
6.3
 
 
 ...
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