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One - One function

If fx = a |...

Question

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

a = b = c = 0

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

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b = c = 0, a \in R

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

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Solution

The correct option is A $a = 0, b = 0, c \in R$
$| sin x |$ and $e^{| x |}$ are not differentiable at $x = 0$ and $| x^{3} |$ is differentiable at $x = 0.$
Therefore, for $f (x)$ to be differentiable at $x = 0$ , we must have $a = 0, b = 0$ and c can be any real number.

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