Continuity and DifferentiabilityHard
Question
The function f (x) = 1 + |sin x| is
Options
A.continuous no where
B.continuous everywhere
C.differentiable at x = 0
D.not differentiable at infinite number of points.
Solution
We know, f (x) = 1 + | sin x | could be plotted as.
(1) y = sin x ....(i)
(2) y =| sin x | ....(ii)
(3) y =1+ | sin x | ....(iii)
Clearly, y = 1+ | sin x | is continuous for all x, but not differentiable at infinite number of poinrs.
(1) y = sin x ....(i)
(2) y =| sin x | ....(ii)
(3) y =1+ | sin x | ....(iii)
Clearly, y = 1+ | sin x | is continuous for all x, but not differentiable at infinite number of poinrs.
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