Question:
The function f(x)=(x-1)√|x| is at x=1:
The function f(x)=(x-1)√|x| is at x=1:
Show Hint
Absolute value functions require one-sided derivative check.
Updated On: Mar 18, 2026
- discontinuous
- continuous but not differentiable
- differentiable with f'(1)=0
- differentiable with f'(1)≠0
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The Correct Option is C
Solution and Explanation
Step 1: Continuity. Function is continuous at x=1.
Step 2: Differentiability. Left and right derivatives exist and are equal.
Step 3: Value of derivative. f'(1)=0
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