If f ( x ) = a ∣ sin x ∣ + b e ∣ x ∣ + c ∣ x ∣ 3 , where a , b , c ∈ R , is differentiable at x = 0 , then

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MathematicsContinuity - DifferentiabilityDifferentiabilityMedium2 minPYQ_2012

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If $f (x) = a ∣ sin x ∣ + b e^{∣ x ∣} + c ∣ x ∣^{3}$ , where $a, b, c \in R$ , is differentiable at $x = 0$ , then

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$∣ sin x ∣$ and $e^{∣ x ∣}$ are not differentiable at $x = 0$ and $∣ x ∣^{3}$ is differentiable at $x = 0$ . $∴$ for $f (x)$ to be differentiable at $x = 0$ , we must have $a = 0, b = 0$ and $c$ is any real number.

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Differentiability

⏱ 2mℹ️ Source: PYQ_2012

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