Enter the \( x \)-value at which the function is not differentiable. If there is no such point, enter NA. \[ \begin{array}{c}f(x)=|x-2|+2 \\ x=[\text { ? }]\end{array} \]

To determine the \( x \)-value at which the function \( f(x) = |x - 2| + 2 \) is not differentiable, we need to analyze the absolute value function. 1. **Identify the point of non-differentiability**: The function \( |x - 2| \) is not differentiable at the point where the expression inside the absolute value equals zero. This occurs when: \[ x - 2 = 0 \implies x = 2 \] 2. **Check the behavior around \( x = 2 \)**: - For \( x < 2 \), \( |x - 2| = -(x - 2) = 2 - x \). - For \( x > 2 \), \( |x - 2| = x - 2 \). 3. **Calculate the left-hand and right-hand derivatives at \( x = 2 \)**: - Left-hand derivative (as \( x \) approaches 2 from the left): \[ f'(x) = \frac{d}{dx}(2 - x) = -1 \] - Right-hand derivative (as \( x \) approaches 2 from the right): \[ f'(x) = \frac{d}{dx}(x - 2) = 1 \] 4. **Conclusion**: Since the left-hand derivative and right-hand derivative at \( x = 2 \) are not equal, the function is not differentiable at this point. Thus, the \( x \)-value at which the function is not differentiable is: \[ x = 2 \]