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Mathematics
Mathematics
Problem
For a smooth curve defined parametrically by
x
=
f
(
t
)
x=f(t)
x
=
f
(
t
)
and
y
=
g
(
t
)
y=g(t)
y
=
g
(
t
)
, which of the following conditions indicates that the curve has a vertical tangent line at
t
=
a
t=a
t
=
a
? a)
f
′
(
a
)
=
0
and
g
′
(
a
)
=
0
f'(a)=0\text{ and }g'(a)=0
f
′
(
a
)
=
0
and
g
′
(
a
)
=
0
b)
f
′
(
a
)
=
0
and
g
′
(
a
)
≠
0
f'(a)=0\text{ and }g'(a)\neq 0
f
′
(
a
)
=
0
and
g
′
(
a
)
=
0
c)
f
′
(
a
)
≠
0
and
g
′
(
a
)
=
0
f'(a)\neq 0\text{ and }g'(a)=0
f
′
(
a
)
=
0
and
g
′
(
a
)
=
0
d)
f
′
(
a
)
=
g
′
(
a
)
f'(a)=g'(a)
f
′
(
a
)
=
g
′
(
a
)
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