MATH
220
EXAM
#1
OCTOBER
7,
1997
[10]
1.
Find
the
equation
of
the
line
tangent
to
the
curve
(
2
}3
y
= x
+x+l
at
the
point
where
x
=
0.
6
4
[10]
2.
Find
those
x
at
which
the
curve
y
= x
+
3x
-
2x
is
concave
up.
[15]
3.
A
toy
rocket,
fired
straight
up
into
the
air,
has
height
s(t)
=
-16t
2
+
160t
feet
after
t
seconds.
(a)
At
what
time
will
the
rocket
hit
the
ground?
(b)
At
what
velocity
will
the
rocket
be
traveling
just as
it
smashes
into
the
ground?
[40]
4.
Sketch
the
graph
of
the
following
functions,
indicating
all
extreme
points
and
inflection
points.
SHOW
ALL
WORK.
(a)
y
=
-x3
+
3x
2
-
5
(b)
y
=
2x
3
+
x
-
2
[25]
5.
A
closed
rectangular
box
with
a
square
base
is
to
be
constructed
using
two
different
types
of
wood.
The
top
is
made
of
wood
costing
$3.00
per
square
foot
and
the
remainder
is
made
of
wood
costing
$1.00
per
square
foot.
Suppose
that
#48
is
available
to
spend.
Find
the
dimensions
of
the
box
of
greatest
volume
that
can
be
constructed.
mrh:9/97
a:220xlgol.f97