The function defined by f(x)=max{x2,(x−1)2,2x(1−x)} for 0<x<1
A
is differentiable for all x.
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B
is differentiable for all x except at one point.
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C
is differentiable for all x except at two points.
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D
is not differentiable at more than two points.
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Solution
The correct option is C is differentiable for all x except at two points.
From the above graph, clearly there are two such points where f(x) is not differentiable.