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Problem
Problem
Consider the polynomial function
f
(
x
)
=
x
7
7
−
x
6
6
+
x
5
5
−
x
4
4
+
x
3
3
−
x
2
2
+
x
f(x) = \frac{x^7}{7} - \frac{x^6}{6} + \frac{x^5}{5} - \frac{x^4}{4} + \frac{x^3}{3} - \frac{x^2}{2} + x
f
(
x
)
=
7
x
7
−
6
x
6
+
5
x
5
−
4
x
4
+
3
x
3
−
2
x
2
+
x
Statement I The equation
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
cannot have two or more roots. Statement II Rolle's theorem is not applicable for
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
on any interval
[
a
,
b
]
[a, b]
[
a
,
b
]
, where
a
,
b
∈
R
a, b \in \mathbb{R}
a
,
b
∈
R
.
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