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Limits Continuity and Differentiability question

2016 · Shift 2 · Q36

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2016 · Shift 2 · Q36

Limits Continuity and Differentiability question

2016 · Shift 2 · Q36

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let

f:\left[ { - {1 \over 2},2} \right] \to R

and

g:\left[ { - {1 \over 2},2} \right] \to R

be function defined by

f(x) = [{x^2} - 3]

and

g(x) = |x|f(x) + |4x - 7|f(x)

, where [y] denotes the greatest integer less than or equal to y for

y \in R

. Then

A
f is discontinuous exactly at three points in $\left[ { - {1 \over 2},2} \right]$ .
B
f is discontinuous exactly at four points in $\left[ { - {1 \over 2},2} \right]$ .
C
g is NOT differentiable exactly at four points in $\left( { - {1 \over 2},2} \right)$ .
D
g is NOT differentiable exactly at five points in $\left( { - {1 \over 2},2} \right)$ .

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