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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
3
−
3
x
f(x)=x^{3}-3x
f
(
x
)
=
x
3
−
3
x
for all real
x
x
x
, and define
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
F(x)=\int_{0}^{x} f(t)\,dt
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
. Determine all values of
x
x
x
in
(
−
3
,
3
)
(-3,3)
(
−
3
,
3
)
at which
F
F
F
has a critical point.
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