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Limits Continuity and Differentiability question

2023 · Shift 2 · Q23

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2023 · Shift 2 · Q23

Limits Continuity and Differentiability question

2023 · Shift 2 · Q23

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMultiple correct+4 / −2

Let

f:(0,1) \rightarrow \mathbb{R}

be the function defined as

f(x)=[4 x]\left(x-\frac{1}{4}\right)^2\left(x-\frac{1}{2}\right)

, where

[x]

denotes the greatest integer less than or equal to

x

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

A
The function $f$ is discontinuous exactly at one point in $(0,1)$
B
There is exactly one point in $(0,1)$ at which the function $f$ is continuous but NOT differentiable
C
The function $f$ is NOT differentiable at more than three points in $(0,1)$
D
The minimum value of the function $f$ is $-\frac{1}{512}$

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