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A derivable function satisfies the condition
MATHEMATICS · Single correct · ISC · Mathematics · Physics · Algebra
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 (1) 5050 (2) 5510 (3) 5150 (4) 1550
Related theory
Functions
Linear Inequalities
Solving linear inequations
Inequalities in one variable
Linear Inequations
Special sums
Derivatives of standard functions via chain rule
Calculus for motion
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