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Application of Derivatives question

2007 · Shift 1 · Q24

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2007 · Shift 1 · Q24

Application of Derivatives question

2007 · Shift 1 · Q24

JEE AdvancedMathematicsApplication of DerivativesMCQ+3 / −1

Let

f(x)

be differentiable on the interval (0,

\infty

) such that

f(1)=1

, and

\mathop {\lim }\limits_{t \to x} {{{t^2}f(x) - {x^2}f(t)} \over {t - x}} = 1

for each

x \gt 0

. Then

f(x)

is

A
${1 \over {3x}} + {{2{x^2}} \over 3}$
B
$- {1 \over {3x}} + {{4{x^2}} \over 3}$
C
$- {1 \over x} + {2 \over {{x^2}}}$
D
${1 \over x}$

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