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Mathematics
Mathematics
Problem
Consider the parametric curve
x
(
t
)
=
t
x(t)=t
x
(
t
)
=
t
and
y
(
t
)
=
t
3
−
6
t
2
+
9
t
y(t)=t^{3}-6t^{2}+9t
y
(
t
)
=
t
3
−
6
t
2
+
9
t
for
0
≤
t
≤
5
0\le t\le5
0
≤
t
≤
5
. Find all values of
t
t
t
in this interval at which
d
2
y
d
x
2
=
0
\displaystyle \frac{d^{2}y}{dx^{2}}=0
d
x
2
d
2
y
=
0
.
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