Continuity and DifferentiabilityHard
Question
A function f defined as f (x) = x [x] for -1≤ x ≤ 3 where [x] defines the greatest integer ≤ x is -
Options
A.continuous at all points in the domain of f but non-derivable at a finite number of points
B.discontinuous at all points & hence non-derivable at all points in the domain of f
C.discontinuous at a finite number of points but not derivable at all points in the domain of f
D.discontinuous & also non-derivable at a finite number of points of f
Solution
Since [x] is not continuous at integers so x[x] is also not continuous at finite number of points in [- 1, 3] & hence not continuous.
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