COMEDK · Maths · 25. Continuity and Differentiability
The function \(f(x) = |x| + |x - 1|\) is:
- A Differentiable at \(x = 1\) but not at \(x = 0\)
- B Neither differentiable at \(x = 0\) nor \(x = 1\)
- C Differentiable at \(x = 0\) and \(x = 1\)
- D Differentiable at \(x = 0\) but not at \(x = 1\)
Answer & Solution
Correct Answer
(B) Neither differentiable at \(x = 0\) nor \(x = 1\)
Step-by-step Solution
Detailed explanation
The given function is \(f(x) = |x| + |x - 1|\). We can redefine the function as a piecewise function: \(f(x) = \begin{cases} -x - (x - 1) = -2x + 1, & x < 0 \\ x - (x - 1) = 1, & 0 \le x < 1 \\ x + (x - 1) = 2x - 1, & x \ge 1 \end{cases}\) Checking differentiability at…
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