Consider the greatest integer function, defined by `f(x) =[x],0 le x lt 2`. Then,

Options

A. f is derivable at x = 1
B. f is not derivable at x = 1
C. f is derivable at x = 1
D. None of the above

Answer

B

Explanation

The given function is `f(x) ={ {:(0,0le x lt1),(1,1lex lt 1):}`
Now , LHD `=underset(xto1^(-))lim(f(x)-f(1))/(x-1) = underset(x to 1^(-))lim(0-1)/(x-1) `, which does not exist .
`because ` LHD does not exist .
` rArr r ` is not derivable at x = 1 .