Question

greatest integer function is not differentiable at integral points. give reason

Answer 1

At Integral points the Left Hand Limit of the function is not equal to the Right Hand Limit.
Ex. Greatest integer value of 2.
LHL = lim h- 0f (2-h) = 1(as h is a very small integer greatest integer to the left of 2-h = 1).
RHL = lim h - of (2+h) = 2
Therefore, LHL is not equal to RHL

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