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Differentiation question

2008 · Shift 2 · Q35

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PYQ Library
JEE Advanced
Mathematics
Differentiation
2008 · Shift 2 · Q35

Differentiation question

2008 · Shift 2 · Q35

JEE AdvancedMathematicsDifferentiationMCQ+3 / −1

Let

g(x) = \log f(x)

, where

f(x)

is a twice differentiable positive function on (0,

\infty

) such that

f(x + 1) = xf(x)

. Then for N = 1, 2, 3, ...,

g''\left( {N + {1 \over 2}} \right) - g''\left( {{1 \over 2}} \right) =

A
$- 4\left\{ {1 + {1 \over 9} + {1 \over {25}} + ....... + {1 \over {{{\left( {2N - 1} \right)}^2}}}} \right\}$
B
$4\left\{ {1 + {1 \over 9} + {1 \over {25}} + ....... + {1 \over {{{\left( {2N - 1} \right)}^2}}}} \right\}$
C
$- 4\left\{ {1 + {1 \over 9} + {1 \over {25}} + ....... + {1 \over {{{\left( {2N + 1} \right)}^2}}}} \right\}$
D
$4\left\{ {1 + {1 \over 9} + {1 \over {25}} + ....... + {1 \over {{{\left( {2N + 1} \right)}^2}}}} \right\}$

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