The CARBOXYLIC GROUP contains an O and an -OH on the same end carbon.
All their names end in ...oic acid.
Names would look like ethanoic acid.

No numbering is required for the =O and -OH groups since they are always at the first carbon.

Here is an example of a carboxylic acid.
Notice the carbon chain in RED, and that there is a =O and -OH at the SAME end carbon.

propanoic cid

Step 1
The road is 3 carbons long.
Now 3 carbons = propan
Notice that the numbering starts where the O and OH is.

Step 2
Then we notice the O and OH and recognize that this is a carboxylic acid.
Hence the name must end in oic acid

We combine propan and oic acid.

Step 3
Hence the name is propanoic acid