Question

Discuss the differentiability of f(x) = x|x| at x = 0.​

Answer 1

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Answer 2

Answer:

0

Step-by-step explanation:

Obviously answer is Zero

Because

Here,

X= 0

f(x) = X\X\

Now,

LHS at X = 0

Lim. =f(x)-f(0)

x-->0---------------

X-0

Lim

x----->0 = -X = 0 ( x^2 will gets cancel)

Now,

RHS at X = 0

Lim. = f(x) - f(0)

------------------------

x-->0 = X-0

So,

Lim

X----->0 = X = 0

So,

Lim (LHS and RHS ) = X = 0

So

The answer is Zero

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