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Limits Continuity and Differentiability question

2015 · Shift 1 · Q39

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2015 · Shift 1 · Q39

Limits Continuity and Differentiability question

2015 · Shift 1 · Q39

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let

g:R \to R

be a differentiable function with

g(0) = 0

,

g'(0) = 0

and

g'(1) e 0

. Let

f(x) = \left\{ {\begin{matrix} {{x \over {|x|}}g(x),} & {x e 0} \\ {0,} & {x = 0} \\ \end{matrix} } \right.

and

h(x) = {e^{|x|}}

for all

x \in R

. Let

(f\, \circ \,h)(x)

denote

f(h(x))

and

(h\, \circ \,f)(x)

denote

f(f(x))

. Then which of the following is (are) true?

A
f is differentiable at x = 0.
B
h is differentiable at x = 0.
C
$f\, \circ \,h$ is differentiable at x = 0.
D
$h\, \circ \,f$ is differentiable at x = 0.

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