The function $$f(x) = 2x + |x - 1| \quad \text{at } x = 1 \text{ is}$$​​

Correct option is B

​$$\text{Solution: }\\ f(x) = 2x + |x - 1| \\[6pt]\text{Case 1: } x > 1 \Rightarrow f(x) = 2x + (x - 1) = 3x - 1 \\[4pt]\text{Case 2: } x < 1 \Rightarrow f(x) = 2x - (x - 1) = x + 1 \\[8pt]\text{Left-hand derivative at } x = 1: f'(x) = 1 \\\text{Right-hand derivative at } x = 1: f'(x) = 3 \\[8pt]\text{Since } f'_L(1) \ne f'_R(1), \text{ function is not differentiable at } x = 1 \\[6pt]\text{However, } f(x) \text{ is continuous at } x = 1 \\[12pt]\boxed{\text{Correct answer: (B) Continuous}}$$​​