Question:
The derivative of $ f(x) = |x| $ at $ x = 0 $ is
The derivative of $ f(x) = |x| $ at $ x = 0 $ is
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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).
Updated On: Apr 11, 2025
- 0
- 1
- -1
- None of these
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The Correct Option is D
Solution and Explanation
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.
Thus, the correct answer is (d) None of these.
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