If f(x) = cases -x - 2 , & x - 2 - x, & - 2 1, cases then

JEE Advanced 2011 Mathematics question

f(x) =

then

(A)f(x) is continuous at Correct
(B)f(x) is not differentiable at x = 0Correct
(C)f(x) is differentiable at x = 1Correct
(D)f(x) is differentiable at Correct

Answer: (A),(B),(C),(D)

Solution

(A) At : left value ; right limit . Continuous. True. (B) At x = 0: and the right limit is , so f is continuous; left derivative , right derivative . They differ, so f is not

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Question ID VK-025992