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$If f (x) = |x| e^{x} then at x = 0$

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f is continuous

f is continuous but not differentiable

f is differentiable

the derivative is 1

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detailed solution

Correct option is B

L.H.D. =Ltx→0−⁡−xexx=−1, R.H.D. =Ltx→0+xexx=1f is continuous but not differentiable.

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If f(x)=xex then at x=0

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$If f (x) = |x| e^{x} then at x = 0$