JEE Main 2021 (25 July Morning Shift)

Question

Let $f:[0,\infty ) 	o [0,\infty )$ be defined as $f(x) = \int_0^x {[y]dy} $ where [x] is the greatest integer less than or equal to x. Which of the following is true?

Accepted Answer

$f$ is continuous at every point in $[0, \infty)$ and differentiable …

Answer

$f$ is both continuous and differentiable except at the integer point…

Answer

$f$ is continuous everywhere except at the integer points in $[0, \in…

Answer

$f$ is differentiable at every point in $[0, \infty)$.

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