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Mathematics
Problem
Let
g
(
x
)
=
x
3
−
5
x
+
2
g(x)=x^{3}-5x+2
g
(
x
)
=
x
3
−
5
x
+
2
be defined on the closed interval
[
−
2
,
3
]
[-2,3]
[
−
2
,
3
]
. Explain why there must exist at least one number
c
c
c
in
(
−
2
,
3
)
(-2,3)
(
−
2
,
3
)
such that
g
′
(
c
)
=
2
g'(c)=2
g
′
(
c
)
=
2
.
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