First slide

Differentiability

Question

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

Moderate

A

$f is continuous$
B

$f is continuous but not differentiable$
C

$f is differentiable$
D

$t h e d e r i v a t i v e i s 1$

Solution

$L.H.D. = {Lt}_{x \to 0^{-}} \frac{- x e^{x}}{x} = - 1, R.H.D. = L t_{x \to 0^{+}} \frac{x e^{x}}{x} = 1$
$f is continuous but not differentiable.$

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