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Limits Continuity and Differentiability question

2016 · Shift 2 · Q34

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2016 · Shift 2 · Q34

Limits Continuity and Differentiability question

2016 · Shift 2 · Q34

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let a, b

\in

R and f : R

\to

R be defined by

f(x) = a\cos (|{x^3} - x|) + b|x|\sin (|{x^3} + x|)

. Then f is

A
differentiable at x = 0 if a = 0 and b = 1.
B
differentiable at x = 1 if a = 1 and b = 0.
C
NOT differentiable at x = 0 if a = 1 and b = 0.
D
NOT differentiable at x = 1 if a = 1 and b = 1.

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