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Mathematics
Problem
## EXERCISE 12.2 5. For the function
f
(
x
)
=
x
100
100
+
x
99
99
+
…
+
x
2
2
+
x
+
1
f(x)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+\ldots+\frac{x^{2}}{2}+x+1
f
(
x
)
=
100
x
100
+
99
x
99
+
…
+
2
x
2
+
x
+
1
Prove that
f
′
(
1
)
=
100
f
′
(
0
)
f^{\prime}(1)=100 f^{\prime}(0)
f
′
(
1
)
=
100
f
′
(
0
)
.
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