Show that ƒ(x) = [x] is neither continuous nor derivable at x=2.

Question

Philoid · Accepted Answer

Left hand limit at x = 2

Right hand limit at x = 2

As left hand limit ≠ right hand limit

Therefore, f(x) is not continuous at x = 2

Lets see the differentiability of f(x):

LHD at x = 2

RHD at x = 2

As, LHD ≠ RHD

Therefore,

f(x) is not derivable at x = 2