Question:
If \( f(x) = |x| - |1| \), then points where \( f(x) \) is not differentiable, is/are:
If \( f(x) = |x| - |1| \), then points where \( f(x) \) is not differentiable, is/are:
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A function is not differentiable at points where sharp corners, vertical tangents, or discontinuities occur.
Updated On: Apr 15, 2025
- \( 0, 1 \)
- \( \pm 1, 0 \)
- \( 0 \)
- \( 1 \text{ only} \)
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The Correct Option is B
Solution and Explanation
Consider the function \( f(x) = ||x| - 1| \) and analyze the transformations step by step:
First, examine \( y = |x| \):
\[
\text{The graph of } y = |x| \text{ has a sharp corner at } x = 0.
\]
Next, for \( y = |x| - 1 \):
\[
\text{The graph shifts vertically downward by 1 unit.}
\]
Finally, for \( f(x) = ||x| - 1| \):
\[
\text{Sharp corners are formed at } x = \{-1, 0, 1\}.
\]
Thus, \( f(x) \) is not differentiable at the points \( \{-1, 0, 1\} \).
Final Answer:
\[
\boxed{\pm 1, 0}
\]
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