First slide

Differentiability

Question

$If f (x) = \{\begin{array}{cc} 1, & x < 0 \\ 1 + \sin x, 0 \leq x < \frac{π}{2}, Then f^{'} (0) i s \end{array}$

Moderate

A

-1
B

0
C

1
D

does not exist

Solution

$\begin{array}{l} L . H . D . a t x = 0 i s {[\frac{d}{d x} (1)]}_{x = 0} = 0 \\ R . H . D a t x = 0 i s {[\frac{d}{d x} (1 + \sin x)]}_{x = 0} = \cos 0 = 1. \\ ∴ f' (x) d o e s n o t e x i s t . \end{array}$

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