Question

If \(f(x) = |x - 1|\), then

• A. \( f(x) \) is differentiable at \(x = 1\)
• B. \( f(x) \) is not differentiable at \(x = 1\)
• C. \( f(x) \) is not differentiable at \(x = 0\)
• D. \( f(x) \) is not continuous at \(x = 0\)

Hint:

For functions involving absolute value, check for points where the function has a "corner" or change in slope. These points may not be differentiable.

Answer 1

The Correct Option is B

The function \(f(x) = |x - 1|\) is not differentiable at \(x = 1\) because there is a sharp corner at this point. The derivative of \(f(x)\) does not exist at \(x = 1\) due to the discontinuity in the slope. The function is continuous but not differentiable at this point.