Question

For a real number y, let [y] denotes the greatest integer less than or equal to y. Then, the function

(a) discontinuous at some x

(b) continuous at all x, but the derivative f'(x) does not exist for some x.

(c) f'(x) exists for all x, but the derivative f''(x) does not exist for some x

(d) f'(x) exists for all x

Answer 1

Correct option (d) f'(x) exists for all x

Explanation :

Here,

Since, we know

Thus, f(x) is a constant function.

.'. f'(x), f''(x) ... all exist for every x, their value being 0.

f'(x) exists for all x.