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Differentiation question

2016 · Shift 1 · Q26

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PYQ Library
JEE Advanced
Mathematics
Differentiation
2016 · Shift 1 · Q26

Differentiation question

2016 · Shift 1 · Q26

JEE AdvancedMathematicsDifferentiationMultiple correct+4 / −2

Let

f:\mathbb{R} \to \mathbb{R},\,g:\mathbb{R} \to \mathbb{R}

and

h:\mathbb{R} \to \mathbb{R}

be differentiable functions such that

f\left( x \right)= {x^3} + 3x + 2,g\left( {f\left( x \right)} \right) = x

and

h\left( {g\left( {g\left( x \right)} \right)} \right) = x

for all

x \in R

. Then

A
$g'\left( 2 \right) = {1 \over {15}}$
B
$h'\left( 1 \right) = 666$
C
$h\left( 0 \right) = 16$
D
$h\left( {g\left( 3 \right)} \right) = 36$

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