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Question

# Let f:[0,∞)→[0,3] be a function defined by f(x)={max{sint:0≤t≤x},0≤x≤π2+cosx,x>π Then which of the following is true?

A
f is continuous everywhere but not differentiable exactly at two points in (0,)
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B
f is continuous everywhere but not differentiable
exactly at one point in (0,)
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C
f is differentiable everywhere in (0,)
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D
f is not continuous exactly at two points in (0,)
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Solution

## The correct option is C f is differentiable everywhere in (0,∞)f:[0,∞)→[0,3] and f(x)={max{sint:0≤t≤x},0≤x≤π2+cosx,x>π Clearly f(x) is continuous everywhere and f(x) is differentiable at x=π2 and x=π ∴f(x) is differentiable everywhere

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