Without using derivative, find the maximum value and the minimum value, if any, of the function f defined by
f(x)=3+|x+1|, `x in R`

Explanation

To find the maximum and minimum values of the function \( f(x) = 3 + |x + 1| \) without using derivatives, we can analyze the properties of the absolute value function.

### Step-by-Step Solution:

1. **Understanding the Absolute Value**:
The absolute value function \( |x + 1| \) represents the distance of \( x + 1 \) from 0 on the number line. This means that \( |x + 1| \) is always non-negative:
\[
|x + 1| \geq 0 \quad \text{for all } x \in \mathbb{R}
...