First slide

Differentiability

Question

$If f (x) = a | \sin x | + b e^{| x |} + c | x |^{3} andif f (x) is differentiableat x = 0,then$

Moderate

A

$a = b = c = 0$
B

$a = b = 0, c \in R$
C

$b = c = 0, a \in R$
D

$a = c = 0, b \in R .$

Solution

$\begin{array}{l} F o r x \neq 0, f (x) = x^{2} + \frac{\frac{x^{2}}{1 + x^{2}}}{1 - \frac{1}{1 + x^{2}}} = x^{2} + 1 \\ A l s o, f (0) = 0. \\ ∴ f (x) i s d i s c o n t i n u o u s a t x = 0. \end{array}$

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