Let $f\left( x \right) = \mathop \smallint \limits_0^x \,\,\left| {x - 2} \right|\,\,dx,\,\,x \ge 0$. Then, $f'\,\,\left( x \right)$ is

Neither continuous nor differentiable at $x = 2$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f\left( x \right) = \int \limits_0^x \,\,\left| {x - 2} \right|\,\,dx,\,\,x \ge 0

. Then,

f'\,\,\left( x \right)

View answer and explanation

Correct option: A

Continuous and non differentiable at

x = 2

Option A (Continuous and non differentiable at

x = 2

) is correct because the derivative is an absolute value function, which is continuous but not differentiable at the point where the expression inside the absolute value is zero.

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