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

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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:
$$
x = 2
$$
The function is not differentiable at $$ x = 2 $$.

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

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