COMEDK · Maths · 25. Continuity and Differentiability
The function \(y = ||x| - 1|\) is differentiable for all values of '\(x\)' except
- A \(\{-1 , 0 , 1\}\)
- B \(\{-1\}\)
- C \(\{0 , 1\}\)
- D \(\{-1 , 1\}\)
Answer & Solution
Correct Answer
(A) \(\{-1 , 0 , 1\}\)
Step-by-step Solution
Detailed explanation
The given function is \(y = ||x| - 1|\). A function of the form \(|f(x)|\) is generally non-differentiable at points where \(f(x) = 0\) (if the curve crosses the x-axis) and at points where \(f(x)\) itself is non-differentiable. First, the inner function \(f(x) = |x| - 1\)…
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