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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
k
x
3
+
m
x
f(x)=k x^{3}+m x
f
(
x
)
=
k
x
3
+
m
x
, where
k
k
k
and
m
m
m
are constants. The function satisfies
f
(
1
)
=
11
3
,
(
f
−
1
)
′
(
11
3
)
=
1
5
,
and
(
f
−
1
)
′
(
0
)
=
1
3
f(1)=\dfrac{11}{3},\quad (f^{-1})'\!\left(\dfrac{11}{3}\right)=\dfrac{1}{5},\quad\text{and}\quad (f^{-1})'(0)=\dfrac{1}{3}
f
(
1
)
=
3
11
,
(
f
−
1
)
′
(
3
11
)
=
5
1
,
and
(
f
−
1
)
′
(
0
)
=
3
1
. Determine the values of
k
k
k
and
m
m
m
.
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