Choose the function whose graph is given by: OA. y= cos(2x)
OB. y= cos(1/2x)
OC. y= cos(4x)
D. y = cos(1/4x)

Explanation:
Note that
d
d
x
(
arccos
(
x
)
)
=
−
1
√
1
−
x
2
.
Then, by the chain rule
d
d
x
(
arccos
(
4
x
2
)
)
=
2
⋅
(
arccos
(
4
x
2
)
)
⋅
d
d
x
(
arccos
(
4
x
2
)
)
.
Then, by the chain rule again,
d
d
x
(
arccos
(
4
x
2
)
)
=
−
1
√
1
−
16
x
4
⋅
d
d
x
(
4
x
2
)
,
d
d
x
(
arccos
(
4
x
2
)
)
=
−
8
x
√
1
−
16
x
4
.
Substituting,
d
d
x
(
arccos
(
4
x
2
)
)
=
−
16
x
⋅
arccos
(
4
x
2
)
√
1
−
16
x
4
.

The slope best fit isc. 1/6 mile per hour