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Mathematics
Mathematics
Problem
Let
x
(
t
)
=
t
x(t)=t
x
(
t
)
=
t
and
y
(
t
)
=
t
4
−
4
t
2
y(t)=t^{4}-4t^{2}
y
(
t
)
=
t
4
−
4
t
2
for all real
t
t
t
. Determine the coordinates of every point of inflection of the curve. a)
(
±
2
,
−
4
)
(\pm\sqrt{2},-4)
(
±
2
,
−
4
)
b)
(
±
6
3
,
−
20
9
)
\left(\pm\dfrac{\sqrt6}{3},-\dfrac{20}{9}\right)
(
±
3
6
,
−
9
20
)
c)
(
2
3
,
−
128
81
)
\left(\dfrac23,-\dfrac{128}{81}\right)
(
3
2
,
−
81
128
)
d)
(
±
6
3
,
−
2
)
\left(\pm\dfrac{\sqrt6}{3},-2\right)
(
±
3
6
,
−
2
)
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