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Mathematics
Mathematics
Problem
Let
h
(
x
)
=
p
(
x
)
q
(
x
)
h(x)=\dfrac{p(x)}{q(x)}
h
(
x
)
=
q
(
x
)
p
(
x
)
, where
p
p
p
and
q
q
q
are differentiable and
q
(
x
)
≠
0
q(x)\neq0
q
(
x
)
=
0
for all
x
x
x
. For
h
h
h
to have a horizontal tangent at
x
=
a
x=a
x
=
a
, which of the following conditions must be satisfied? a)
p
′
(
a
)
=
0
p'(a)=0
p
′
(
a
)
=
0
b)
p
′
(
a
)
q
′
(
a
)
=
0
p'(a)q'(a)=0
p
′
(
a
)
q
′
(
a
)
=
0
c)
p
′
(
a
)
q
(
a
)
−
p
(
a
)
q
′
(
a
)
=
0
p'(a)q(a)-p(a)q'(a)=0
p
′
(
a
)
q
(
a
)
−
p
(
a
)
q
′
(
a
)
=
0
d)
p
(
a
)
=
0
p(a)=0
p
(
a
)
=
0
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