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Mathematics
Mathematics
Problem
Explain why a parametric curve
(
x
(
t
)
,
y
(
t
)
)
\bigl(x(t),\,y(t)\bigr)
(
x
(
t
)
,
y
(
t
)
)
has a vertical tangent at a value
t
=
a
t=a
t
=
a
when
d
x
d
t
∣
t
=
a
=
0
\left.\dfrac{dx}{dt}\right|_{t=a}=0
d
t
d
x
t
=
a
=
0
while
d
y
d
t
∣
t
=
a
≠
0
\left.\dfrac{dy}{dt}\right|_{t=a}\neq 0
d
t
d
y
t
=
a
=
0
.
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