Section 6.3
Extrema and Models
593
Version: Fall 2007
6.3
Exercises
In
Exercises 1

8
, perform each of the
following tasks for the given polynomial.
i.
Without the aid of a calculator, use
an algebraic technique to identify the
zeros of the given polynomial. Factor
if necessary.
ii.
On graph paper, set up a coordinate
system.
Label each axis, but scale
only the
x
axis.
Use the zeros and
the endbehavior to draw a “rough
graph” of the given polynomial with
out the aid of a calculator.
iii. Classify each local extrema as a
rela
tive minimum
or
relative maximum
.
Note: It is not necessary to find the
coordinates of the relative extrema.
Indeed, this would be difficult with
out a calculator. All that is required
is that you label each extrema as a
relative maximum or minimum.
1.
p
(
x
) = (
x
+ 6)(
x
−
1)(
x
−
5)
2.
p
(
x
) = (
x
+ 2)(
x
−
4)(
x
−
7)
3.
p
(
x
) =
x
3
−
6
x
2
−
4
x
+ 24
4.
p
(
x
) =
x
3
+
x
2
−
36
x
−
36
5.
p
(
x
) = 2
x
3
+ 5
x
2
−
42
x
6.
p
(
x
) = 2
x
3
−
3
x
2
−
44
x
7.
p
(
x
) =
−
2
x
3
+ 4
x
2
+ 70
x
8.
p
(
x
) =
−
6
x
3
−
21
x
2
+ 90
x
In
Exercises 9

16
, perform each of the
following tasks for the given polynomial.
i.
Use a graphing calculator to draw the
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1
graph of the polynomial. Adjust the
viewing window so that the extrema
or “turning points” of the polynomial
are visible in the viewing window. Copy
the resulting image onto your home
work paper.
Label and scale each
axis with xmin, xmax, ymin, and ymax.
ii.
Use the
maximum
and/or
minimum
util
ity in your calculator’s
CALC
menu to
find the coordinates of the extrema.
Label each extremum on your home
work copy with its coordinates and
state whether the extremum is a rel
ative or absolute maximum or mini
mum.
9.
p
(
x
) =
x
3
−
8
x
2
−
5
x
+ 84
10.
p
(
x
) =
x
3
+ 3
x
2
−
33
x
−
35
11.
p
(
x
) =
−
x
3
+ 21
x
−
20
12.
p
(
x
) =
−
x
3
+ 5
x
2
+ 12
x
−
36
13.
p
(
x
) =
x
4
−
50
x
2
+ 49
14.
p
(
x
) =
x
4
−
29
x
2
+ 100
15.
p
(
x
) =
x
4
−
2
x
3
−
39
x
2
+ 72
x
+ 108
16.
p
(
x
) =
x
4
−
3
x
3
−
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 Fermat's theorem, homework paper, Extrema and Models, empirical domain

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