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Mathematics
Problem
A derivable function
f
:
R
+
→
R
f: \mathbb{R}^+ \to \mathbb{R}
f
:
R
+
→
R
satisfies the condition
f
(
x
)
−
f
(
y
)
≥
log
(
x
y
)
+
x
−
y
,
∀
x
,
y
∈
R
+
f(x) - f(y) \ge \log\left(\frac{x}{y}\right) + x - y, \forall x, y \in \mathbb{R}^+
f
(
x
)
−
f
(
y
)
≥
lo
g
(
y
x
)
+
x
−
y
,
∀
x
,
y
∈
R
+
. If
g
g
g
denotes the derivative of
f
f
f
, then the value of the sum
∑
n
=
1
100
g
(
1
n
)
\sum_{n=1}^{100} g\left(\frac{1}{n}\right)
∑
n
=
1
100
g
(
n
1
)
is a. 5050 b. 5510 c. 5150 d. 1550
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