Let R be the set of all real numbers and...

Let R be the set of all real numbers and `f:[-1,1]to R` be defined by `f(x)={{:(xsin""(1)/(x),"where "xne0),(0,"where "x=0):}`, then-

A

f satisfies the conditions of Rolle's theorem of `[-1,1]`

B

f satisfies the conditions of Lagrange's mean value theorem on `[-1,1]`

C

f satisfies the conditions of Rolle's theorem on `[0,1]`

D

f satisfies the conditions of Lagrange's mean value theorem on [0, 1]

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