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Question

Let f(x) = {1 + sin x, x < 0x2 x + 1, x 0. Then

A
f has a local maximum at x = 0
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B
f has a local minimum at x = 0
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C
f is increasing every where
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D
f is decreasing everywhere
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Solution

The correct option is A f has a local maximum at x = 0

f is continuous at ‘0’ and f' (0-) > 0 and f' ( 0 +) < 0 . Thus f has a local maximum at ‘0’.


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