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Question -

Prove that the greatest integer function defined byis not

differentiableat x = 1 and x = 2.



Answer -

The given function f is

It isknown that a function f is differentiable at a point x = c inits domain if both.

are finite and equal.

Tocheck the differentiability of the given function at x = 1,consider the left hand limit of f at x = 1

Sincethe left and right hand limits of f at x = 1are not equal, f is not differentiable at

x = 1

Tocheck the differentiability of the given function at x = 2,consider the left hand limit

of f at x =2

Sincethe left and right hand limits of f at x = 2are not equal, f is not differentiable at x =2

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