First slide

Differentiability

Question

$The function f (x) = (x - 1) | x - 1 | + \sin (| x |) is$

Moderate

A

$differentiable for all x \in R - {1}$
B

$discontinuous at x = 1$
C

$differentiable for all x \in R - {0}$
D

$differentiable for all x$

Solution

$Functions in | x | is not differentiable at x = 0 b u t x |x| i s d i f f e r e n t i a b l e \forall x$
$\begin{array}{l} Function (x - 1) | x - 1 | is differentiable at all points. \\ So, function f (x) = | x - 1 | (x - 1) + \sin | x | is not differentiable at x = 0 only. \end{array}$

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