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Mathematics
Problem
The function
h
h
h
is defined by
h
(
x
)
=
k
x
x
+
2
h(x)=\dfrac{k x}{x+2}
h
(
x
)
=
x
+
2
k
x
, where the constant
k
k
k
is chosen so that the point
(
1
,
1
3
)
(1,\,\tfrac13)
(
1
,
3
1
)
lies on the graph of
h
h
h
. Determine the slope of the tangent line to the graph of
h
h
h
at
x
=
1
x=1
x
=
1
.
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