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Differentiation question

2008 · Shift 1 · Q31

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PYQ Library
JEE Advanced
Mathematics
Differentiation
2008 · Shift 1 · Q31

Differentiation question

2008 · Shift 1 · Q31

JEE AdvancedMathematicsDifferentiationMCQ+3 / −1

Consider the functions defined implicitly by the equation

y^3-3y+x=0

on various intervals in the real line. If

x\in(-\infty,-2)\cup(2,\infty)

, the equation implicitly defines a unique real valued differentiable function

y=f(x)

. If

x\in(-2,2)

, the equation implicitly defines a unique real valued differentiable function

y=g(x)

satisfying

g(0)=0

If

f\left( { - 10\sqrt 2 } \right) = 2\sqrt 2 ,

then

f''\left( { - 10\sqrt 2 } \right) =

A
${{4\sqrt 2 } \over {{7^3}{3^2}}}$
B
$-{{4\sqrt 2 } \over {{7^3}{3^2}}}$
C
${{4\sqrt 2 } \over {{7^3}3}}$
D
$-{{4\sqrt 2 } \over {{7^3}3}}$

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