First slide

Differentiability

Question

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

Moderate

A

Continuous at x = 1 , but not differentiable
B

Continuous as well as differentiable at x = 1
C

not continuous at x = 1
D

none of these.

Solution

$f (x) = \{\begin{cases} - 2 x + 1 x < 0 \\ 1 0 \leq x < 1 \\ 2 x - 1, x \geq 1 \end{cases}$
$Check that f is continuous at x = 1 but it not differentiable at x = 1$

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