The derivative of f x x 3 at x 0 is ........

The derivative of f(x) =|x|³ at x = 0 is

-1

not defined

1/2

- The derivative of \( f(x) = |x|^3 \) involves finding the derivative of its expression.

- For \( x > 0 \), \( f(x) = x^3 \) and its derivative is \( 3x^2 \).

- For \( x < 0 \), \( f(x) = (-x)^3 = -x^3 \) and its derivative is \( -3x^2 \).

- At \( x = 0 \), the left-hand and right-hand derivatives are both 0.

- Both sides match, so the derivative at \( x = 0 \) is indeed defined and equals 0.

Option 3: 0

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