ANSWERS PAMPHLET
1
Chapter 2
2.1
i
)
y
5
3
x
2
2 is increasing everywhere, and has no local maxima or minima.
See ﬁgure.*
ii
)
y
52
2
x
is decreasing everywhere, and has no local maxima or minima.
See ﬁgure.
iii
)
y
5
x
2
1
1 has a global minimum of 1 at
x
5
0. It is decreasing on
(
2‘
,
0) and increasing on (0
,
‘
). See ﬁgure.
iv
)
y
5
x
3
1
x
is increasing everywhere, and has no local maxima or minima.
See ﬁgure.
v
)
y
5
x
3
2
x
ha
saloca
lmax
imumo
f2
6
3
p
3a
t
2
1
6
p
3, and a local
minimum of
2
2
6
3
p
t1
6
p
3, but no global maxima or minima. It
increases on (
2‘
,
2
1
6
p
3) and (1
6
p
3
,
‘
) and decreases in between. See
ﬁgure.
vi
)
y
5

x

decreases on (
2‘
,
0) and increases on (0
,
‘
). It has a global
minimum of 0 at
x
5
0. See ﬁgure.
2.2
Increasing functions include production and supply functions. Decreasing
functions include demand and marginal utility. Functions with global critical
points include average cost functions when a ﬁxed cost is present, and proﬁt
functions.
2.3
1, 5,
2
2, 0.
2.4
a
)
x
±
1;
b
)
x
.
1;
c
)a
l
l
x
;
d
)
x
±6
1;
e
)
2
1
#
x
#1
1;
f
)
2
1
#
x
1,
x
±
0.
2.5
a
)
x
±
1,
b
l
l
x
,
c
)
x
±2
1
,
2
2,
d
l
l
x
.
2.6
The most common functions students come up with all have the nonnegative
real numbers for their domain.
2.8
a
)1
,
b
)
2
1,
c
)0
,
d
)3
.
2.8
a
) The general form of a linear function is
f
(
x
)
5
mx
1
b
, where
b
is the
y
intercept and
m
is the slope. Here
m
5
2and
b
5
3, so the formula is
f
(
x
)
5
2
x
1
3.
b
) Here
m
3and
b
5
0, so the formula is
f
(
x
)
3
x
.
*All ﬁgures are included at the back of the pamphlet.