(B) Critical points are the points where $f'(x) = 0$ or where $f(x)$ is not differentiable. For $x 0$,$f'(x) = -3 \n

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Critical points are the points where $f'(x) = 0$ or where $f(x)$ is not differentiable. For $x For $x > 0$,$f'(x) = -3 \neq 0$. Now,check for differentiability at $x = 0$: Left-hand derivative $(LHD)$ at $x = 0$: $\lim_{h \to 0^-} \frac{f(0+h) - f(0)}{h} = \lim_{h \to 0^-} \frac{(1+h) - 2}{h} = \lim_{h \to 0^-} \frac{h-1}{h} = \infty$. Since the derivative does not exist at $x = 0$,$x = 0$ is a critical point.