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Mathematics
Problem
The function
f
(
x
)
=
x
3
−
3
x
x
2
+
1
f(x)=\dfrac{x^{3}-3x}{x^{2}+1}
f
(
x
)
=
x
2
+
1
x
3
−
3
x
is defined for all real
x
x
x
. Which ordered pair best represents the number of horizontal tangents (first entry) and vertical tangents (second entry) of the graph of
f
f
f
? a)
(
1
,
0
)
(1,0)
(
1
,
0
)
b)
(
2
,
1
)
(2,1)
(
2
,
1
)
c)
(
2
,
0
)
(2,0)
(
2
,
0
)
d)
(
0
,
0
)
(0,0)
(
0
,
0
)
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