Let $$f(x) = \left\{ {\matrix{ {{x^2}\left| {\cos {\pi \over x}} \right|,} & {x \ne 0} \cr {0,} & {x = 0} \cr } } \right.$$ x$$\in$$R, then f is

differentiable at x = 0 but not differentiable at x = 2.

JEE Advanced · Quantitative Aptitude

JEE Advanced Differentiability Questions with Answers and Solutions

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JEE Advanced Differentiability practice

Topic-wise practice20 questions 20 min

1Preview question 1 of 5 · instant answer reveal

Let

f:(a,b) \to [1,\infty )

be a continuous function and

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

be defined as

$x$	$g(x)$
$x < a$	$0$
$a \le x \le b$	$\int_a^x f(t) \, dt$
$x > b$	$\int_a^b f(t) \, dt$

Then, i.

g(x)

is continuous but not differentiable at

a

ii.

g(x)

is differentiable on

\mathbb{R}

iii.

g(x)

is continuous but not differentiable at

b

iv.

g(x)

is continuous and differentiable at either

a

b

but not both

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JEE Advanced Differentiability practice FAQ

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JEE Advanced Differentiability practice

What visitors can use on this page

JEE Advanced Differentiability practice FAQ

Prepare together, not alone

JEE Advanced Differentiability practice

What visitors can use on this page

JEE Advanced Differentiability practice FAQ