Question

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

• A. 0
• B. 1
• C. -1
• D. None of these

Hint:

For absolute value functions, check the differentiability at the point where the function has a "corner" (i.e., where the left-hand and right-hand derivatives differ).

Answer 1

The Correct Option is D

The function \( f(x) = |x| \) is not differentiable at \( x = 0 \) because the left-hand and right-hand derivatives do not match. The left-hand derivative is \( -1 \) (approaching from the negative side). The right-hand derivative is \( 1 \) (approaching from the positive side). Since the derivatives do not match, the derivative at \( x = 0 \) does not exist. Conclusion.
Thus, the correct answer is (d) None of these.