(C) Use interval notation to indicate where
f
(
x
)
is decreas
ing.
Decreasing:
(D) List the
x
coordinates of all local maxima of
f
. If there
are no local maxima, enter ’NONE’.
x
values of local maxima =
(E) List the
x
coordinates of all local minima of
f
. If there
are no local minima, enter ’NONE’.
x
values of local minima =
(F) Use interval notation to indicate where
f
(
x
)
is concave
up.
Concave up:
(G) Use interval notation to indicate where
f
(
x
)
is concave
down.
Concave down:
(H) List the
x
values of all in±ection points of
f
. If there are
no in±ection points, enter ’NONE’.
x
values of in±ection points =
Answer(s) submitted:
•
0
•
(0,inf)
•
(inf,0)
•
None
•
0
•
((sqrt(2/9)),(sqrt(2/9)))
•
(inf,sqrt(2)/3)U(sqrt(2)/3,+infinity)
•
(sqrt(2/9)),(sqrt(2/9))
(correct)
4.
(1 pt) Suppose that
f
(
x
)=
x
1
/
3
(
x
+
3
)
2
/
3
(A) Find all critical values of
f
. If there are no critical values,
enter
None
. If there are more than one, enter them separated
by commas.
Critical value(s) =
(B) Use interval notation to indicate where
f
(
x
)
is increasing.
Note:
When using interval notation in WeBWorK, you use
I
for
•
,
I
for

•
, and
U
for the union symbol. If there are no
values that satisfy the required condition, then enter ”” without
the quotation marks.
Increasing:
(C) Use interval notation to indicate where
f
(
x
)
is decreasing.
Decreasing:
(D) Find the
x
coordinates of all local maxima of
f
. If there are
no local maxima, enter
None
. If there are more than one, enter
them separated by commas.
Local maxima at
x
=
(E) Find the
x
coordinates of all local minima of
f
. If there are
no local minima, enter
None
. If there are more than one, enter
them separated by commas.
Local minima at
x
=
(F) Use interval notation to indicate where
f
(
x
)
is concave up.
Concave up:
(G) Use interval notation to indicate where
f
(
x
)
is concave
down.
Concave down:
(H) Find all in±ection points of
f
. If there are no in±ection
points, enter
None
. If there are more than one, enter them sep
arated by commas.
In±ection point(s) at
x
=
Answer(s) submitted:
•
None
•
(1,inf)
•
(inf,1)
•
3
•
None
•
{}
•
{}
•
3,0
(score 0.125)
5.
(1 pt) Suppose that a rectangle has an area of 66 square
meters. Express the perimeter
P
as a function of the length
x
of
one of the sides.
P
(
x
)
=
Answer(s) submitted:
•
(2x)+(132/x)
(correct)
6.
(1 pt) At what value(s) of
x
on the curve
y
=
5
+
90
x
3

3
x
5
does the tangent line have the largest slope?
Answer (separate by commas):
x
=
Answer(s) submitted:
•
3,3
(correct)
7.
(1 pt) The cost of producing
x
units of a product is given
by
C
(
x
)=
500
+
90
x

90ln
(
x
)
,
x
≥
1
.
Find the minimum average cost.
Minimum Average Cost =
Answer(s) submitted:
•
(500/(eˆ(59/9)))+90((90ln(eˆ(59/9)))/(eˆ(59/9)))
(correct)
2