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Mathematics
Mathematics
Problem
Consider the parametrically defined curve
x
=
t
2
−
4
t
2
+
1
x=\dfrac{t^{2}-4}{t^{2}+1}
x
=
t
2
+
1
t
2
−
4
and
y
=
t
3
−
t
y=t^{3}-t
y
=
t
3
−
t
for all real
t
t
t
. At which point does this curve have a vertical tangent line? a)
(
−
11
4
,
−
2
3
3
)
\left(-\dfrac{11}{4},-\dfrac{2}{3\sqrt{3}}\right)
(
−
4
11
,
−
3
3
2
)
b)
(
−
4
,
0
)
(-4,0)
(
−
4
,
0
)
c)
(
0
,
−
4
)
(0,-4)
(
0
,
−
4
)
d)
(
−
3
2
,
0
)
\left(-\dfrac{3}{2},0\right)
(
−
2
3
,
0
)
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