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Mathematics
Mathematics
Problem
Show that the function
f
(
x
)
=
(
x
−
a
)
2
(
x
−
b
)
2
+
x
f(x) = (x-a)^2 (x-b)^2 + x
f
(
x
)
=
(
x
−
a
)
2
(
x
−
b
)
2
+
x
takes the value
a
+
b
2
\frac{a+b}{2}
2
a
+
b
for some value of
x
∈
[
a
,
b
]
x \in [a, b]
x
∈
[
a
,
b
]
.
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