Continuity and DifferentiabilityHard
Question
Consider f (x) = 
; where [ ] denotes the greatest integer function, then -
; where [ ] denotes the greatest integer function, then - Options
A.f is continuous & differentiable at x = π/2
B.f is continuous but not differentiable at x = p/2
C.f is neither continuous not differentiable at x = π/2
D.f is neither continuous not differentiable at x = π/2
Solution
f(x) = 
(∵ sin x > sin3 x in (0, π))
= 3 ; x =
Now f(x) = 3 ; x ≠
= 3 ; x =
Hence f(x) is continuous & differentiable at x =
(∵ sin x > sin3 x in (0, π))
= 3 ; x =
Now f(x) = 3 ; x ≠
= 3 ; x =
Hence f(x) is continuous & differentiable at x =
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