Find the maximum and minimum values , if any , of the function f given by `f(x)=3-|x|`

Explanation

To find the maximum and minimum values of the function \( f(x) = 3 - |x| \), we will analyze the function step by step.

### Step 1: Understand the function
The function \( f(x) = 3 - |x| \) is defined for all real numbers \( x \). The absolute value function \( |x| \) takes on non-negative values, which means \( f(x) \) will decrease as \( |x| \) increases.

### Step 2: Determine the critical points
To find the maximum and minimum values, we first need to find the critical points. The critical points occur where the derivative is zero or undefined.

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