What is the minimum value of |x|?

Options

A. `-1`
B. 0
C. 2
D. 4

Explanation

To find the minimum value of |x|, we can follow these steps:

### Step 1: Define the function
We define the function \( f(x) = |x| \).

### Step 2: Analyze the function
The absolute value function has two cases:
- When \( x \geq 0 \), \( |x| = x \)
- When \( x < 0 \), \( |x| = -x \)

### Step 3: Determine the critical points
To find the minimum value, we need to check the behavior of the function at critical points and endpoints. The function \( f(x) = |x| \) is continuous everywhere, and the only critical point occurs at \( x = 0 \).

### Step 4: Evaluate the function at the critical point
Now we evaluate the function at the critical point:
- \( f(0) = |0| = 0 \)

### Step 5: Check the behavior of the function
For \( x > 0 \), \( f(x) = x \) which is always positive and increasing.
For \( x < 0 \), \( f(x) = -x \) which is also positive and increasing as \( x \) moves away from 0.

### Step 6: Conclusion
Since \( f(x) \) is always greater than or equal to 0 for all \( x \) and reaches its minimum value at \( x = 0 \), we conclude that the minimum value of \( |x| \) is:

\[ \text{Minimum value of } |x| = 0 \]