Test f(x)={x} for the existence of alocal maximum and minimum at x=1, where{.} represents the fractional part function.

Explanation

To determine the existence of a local maximum and minimum for the function \( f(x) = \{x\} \) (where \( \{x\} \) represents the fractional part of \( x \)) at \( x = 1 \), we will analyze the behavior of the function around this point.

### Step 1: Understand the Function
The fractional part function \( f(x) = \{x\} \) can be defined as:
- \( f(x) = x \) for \( 0 \leq x < 1 \)
- \( f(x) = x - 1 \) for \( 1 \leq x < 2 \)

### Step 2: Evaluate \( f(x) \) at \( x = 1 \)
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