Question

If f(x) = |3 – x| + (3 + x), where (x) denotes the least integer greater than or equal to x, then f(x) is

A. continuous and differentiable at x = 3

B. continuous but not differentiable at x = 3

C. differentiable but not continuous at x = 3

D. neither differentiable nor continuous at x = 3

Answer 1

Correct answer is D.

Given that f(x) = |3 – x| + (3 + x), where (x) denotes the least integer greater than or equal to x.

Checking continuity at x = 3,

Here, LHL at x = 3

∴ f(x) is neither continuous nor differentiable at x = 3.