Exams › JEE Main › Maths
At x = 0, which of the following functions is differentiable?
- cos(|x|) + |x|
- cos(|x|) - |x|
- sin(|x|) + |x|
- sin(|x|) - |x|
Correct answer: sin(|x|) - |x|
Solution
cos|x| is smooth but |x| is not, so options 0 and 1 fail. For sin|x|+|x| the one-sided derivatives at 0 are +2 and -2 (fails). For sin|x|-|x| they are 1-1=0 and -1+1=0, equal, so it is differentiable at x=0.
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