The IUPAC name of the compound-
`CH_(3)- underset(OH)underset(|)C=CH-CH_(2)-COOH` is-

Explanation

To determine the IUPAC name of the compound `CH₃-CH(OH)-C=CH-CH₂-COOH`, we can follow these steps:

### Step 1: Identify the longest carbon chain
The first step is to identify the longest continuous carbon chain in the compound. In this case, the longest chain consists of 5 carbon atoms, which includes the carboxylic acid group (COOH).

**Hint:** Look for the longest continuous chain of carbon atoms, including functional groups.

### Step 2: Number the carbon chain
Next, we need to number the carbon chain. The numbering should start from the end of the chain that is closest to the highest priority functional group, which is the carboxylic acid (COOH) in this case. Thus, we will number the carbon chain as follows:

1. COOH (1)
2. CH₂ (2)
3. C (3)
4. C=CH (4)
5. CH(OH) (5)

**Hint:** Always start numbering from the end nearest to the highest priority functional group.

### Step 3: Identify substituents and their positions
In this compound, we have a hydroxyl group (OH) as a substituent on carbon 4.

**Hint:** Identify all substituents and their positions based on the numbering of the carbon chain.

### Step 4: Determine the parent name and functional group suffix
The parent chain consists of 5 carbon atoms, which corresponds to "pentane". Since there is a carboxylic acid group, the suffix will be "oic acid". The presence of the double bond (C=C) indicates that we need to use the "ene" suffix, and since the double bond starts at carbon 3, we will use "3-ene".

**Hint:** The parent name is based on the number of carbons, and the functional groups determine the suffix.

### Step 5: Combine the information to write the IUPAC name
Now we can combine all the information:
- The substituent (hydroxyl group) is on carbon 4, so we write "4-hydroxy".
- The parent chain is "pent" (5 carbons) with a double bond at position 3, so we write "3-pentene".
- The carboxylic acid gives us the suffix "oic acid".

Putting it all together, the IUPAC name of the compound is:
**4-hydroxy-3-pentene-1-oic acid**.

### Final Answer:
**4-hydroxy-3-pentene-1-oic acid**