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Differentiation question

2008 · Shift 2 · Q31

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PYQ Library
JEE Advanced
Mathematics
Differentiation
2008 · Shift 2 · Q31

Differentiation question

2008 · Shift 2 · Q31

JEE AdvancedMathematicsDifferentiationMCQ+3 / −1

Consider the function

f:\left( { - \infty ,\infty } \right) \to \left( { - \infty ,\infty } \right)

defined by

f\left( x \right) = {{{x^2} - ax + 1} \over {{x^2} + ax + 1}},0 \lt a \lt 2.

Which of the following is true?

A
${\left( {2 + a} \right)^2}f''\left( 1 \right) + {\left( {2 - a} \right)^2}f''\left( { - 1} \right) = 0$
B
${\left( {2 - a} \right)^2}f''\left( 1 \right) - {\left( {2 + a} \right)^2}f''\left( { - 1} \right) = 0$
C
$f'\left( 1 \right)f'\left( { - 1} \right) = {\left( {2 - a} \right)^2}$
D
$f'\left( 1 \right)f'\left( { - 1} \right) = -{\left( {2 + a} \right)^2}$

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