Question

Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has

• A. a local maximum
• B. no local maximum
• C. a local minimum
• D. no extremum

Answer 1

Answer: (D)

no extremum

Answer 2

It is clear from figure that at x = 0, f (x) is not differentiable .
$\Rightarrow$ f (x) has neither maximum nor minimum at x = 0