Question

Let \( f(x) = |1 - 2x| \), then

• A. \( f(x) \) is continuous but not differentiable at \( x=\frac{1}{2} \).
• B. \( f(x) \) is differentiable but not continuous at \( x=\frac{1}{2} \).
• C. \( f(x) \) is both continuous and differentiable at \( x=\frac{1}{2} \).
• D. \( f(x) \) is neither differentiable nor continuous at \( x=\frac{1}{2} \).

Hint:

For \( |g(x)| \): \begin{itemize} \item Continuous everywhere. \item Not differentiable where \( g(x)=0 \) and slope changes. \end{itemize}

Answer 1

The Correct Option is A