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  • If   <img alt="\mathrm{f(x)=a|\sin x|+b e^{|x|}+c|x|^3}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3Da%7C%5Csin%20x%7C&plus;b%20e%5E%7B%7Cx%7C%7D&p

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

Option: 1

a=b=c=0


Option: 2

\mathrm{a=0, b=0 ; c \in R}


Option: 3

\mathrm{b=c=0, a \in R}


Option: 4

\mathrm{c=0, a=0, b \in R}


Answers (1)

best_answer

Since |\sin x| and \mathrm{e^{|x|}}  are not 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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HARSH KANKARIA

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