(c) The instantaneous velocity
v(t)
=
$$−400
cos
(
t
)(7+4
sin
(
t
))2
.
(d)
v(pi)
=
$$40049
.
(e) At time
t=pi
, is the object moving RIGHT or LEFT?
(Write answer in caps.)
(f) On the time interval [4,15], what is the first time when the velocity of the object is zero?
(g) On the time interval [4,15], what is the last time when the velocity of the object is zero?

6/5/2019
hw11S3.4
(h) On the time interval [4,15], what is maximum distance from the origin to the object?

5/10

(i) On the time interval [4,15], what is minimum distance from the origin to the object?

8.
4/4 points |
Previous Answers
The graphs of the quadratic functions
f
(
x
) = 6 – 10
x
2
and
g
(
x
) = 8 – (
x
– 2)
2
are provided below.
Observe there are TWO lines simultaneously tangent to both graphs.
(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation:
(Two decimal places of accuracy.)

(b) The other line simultaneously tangent to both graphs has equation:(Two decimal places of
accuracy.)

6/5/2019
hw11S3.4
9.
5/5 points |
Previous Answers
Let
P
be a point on the graph of
y
=
x
3
. The tangent line at
P
will intersect the graph at the point
Q
.
(a) If
P
has
x
coordinate
a
, then what is the equation of the tangent line at
P
:
y=
$$3
a
2
x +
$$−2
a
3
.
(b) The line in (a) will intersect the curve
y
=
x
3
in two places; one of these is
P
and the other
point is:
(
$$−2
a
,
$$−8
a
3
)
(c)The ratio of the slope of the curve at
Q
to the slope at
P
is

6/10
.

6/5/2019
hw11S3.4
7/10
10.
6/6 points |
Previous Answers
Consider this function
y = f(x)
on the domain (
∞
,
∞
).