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Mathematics
Mathematics
Problem
At
x
=
1
x=1
x
=
1
, the functions
f
f
f
and
g
g
g
satisfy
f
(
1
)
=
−
3
,
g
(
1
)
=
5
,
f
′
(
1
)
=
4
f(1)=-3,\;g(1)=5,\;f'(1)=4
f
(
1
)
=
−
3
,
g
(
1
)
=
5
,
f
′
(
1
)
=
4
and
g
′
(
1
)
=
−
2
g'(1)=-2
g
′
(
1
)
=
−
2
. What can be concluded about
h
′
(
1
)
h'(1)
h
′
(
1
)
where
h
(
x
)
=
f
(
x
)
g
(
x
)
h(x)=f(x)g(x)
h
(
x
)
=
f
(
x
)
g
(
x
)
? a)
h
′
(
1
)
=
0
h'(1)=0
h
′
(
1
)
=
0
b)
h
′
(
1
)
h'(1)
h
′
(
1
)
is negative c)
h
′
(
1
)
h'(1)
h
′
(
1
)
is positive d) The sign of
h
′
(
1
)
h'(1)
h
′
(
1
)
cannot be determined
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