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Let $f x = min x, x 2, x ≥ 0 max 2 x, x 2 − 1, x < 0$ . Then which of the following is true?

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f x

is not continuous at

x = 0

f x

is differentiable at

x = 1

f x

is differentiable at exactly three points

f x

is continuous everywhere but not differentiable at

x = 1 − 2, 0, 1

answer is D.

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Detailed Solution

From the graph, it is clear that f(x) is everywhere
continuous but not differentiable at

x = 1 − 2, 0, 1

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