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Mathematics
Mathematics
Problem
Which one of the following conditions guarantees a horizontal tangent to the parametric curve
x
=
f
(
t
)
,
y
=
g
(
t
)
x=f(t),\;y=g(t)
x
=
f
(
t
)
,
y
=
g
(
t
)
at
t
=
t
0
t=t_{0}
t
=
t
0
? a)
f
′
(
t
0
)
=
0
f'(t_{0})=0
f
′
(
t
0
)
=
0
and
g
′
(
t
0
)
≠
0
g'(t_{0})\neq0
g
′
(
t
0
)
=
0
b)
g
′
(
t
0
)
=
0
g'(t_{0})=0
g
′
(
t
0
)
=
0
and
f
′
(
t
0
)
=
0
f'(t_{0})=0
f
′
(
t
0
)
=
0
c)
g
′
(
t
0
)
=
0
g'(t_{0})=0
g
′
(
t
0
)
=
0
and
f
′
(
t
0
)
≠
0
f'(t_{0})\neq0
f
′
(
t
0
)
=
0
d)
f
′
(
t
0
)
=
g
′
(
t
0
)
≠
0
f'(t_{0})=g'(t_{0})\neq0
f
′
(
t
0
)
=
g
′
(
t
0
)
=
0
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