Question

Let ƒ(x) = $\left\{ \begin{array} { c l } | x | & \text { for } 0 < | x | \leq 2 \\ 1 & \text { for } x = 0 \end{array} \right.$ . Then at x = 0, ƒ has –

• A. A local maximum
• B. No local maximum
• C. A local minimum
• D. ) No extremum

Answer 1

)

Sol. Let us redefine the function

x (+ ive) \ |x| = x for 0 < x < 2

x (– ive) \ |x| = –x for 0 < –x < 2

or –2 < x < 0

\ ƒ(x) =

$\frac { d y } { d x }$ does not exist at L.H.D. = –1

and R.H.D. = 1 at x = 0.