I think it need to be like this:
tar -zxvf archive.tar mydirectorytoextract
You have the order correct but I think
you may need the -z option. Watch that -f tho. When you use it, it has to be right before the file name, either as a separate option or on the end like you have them. I ran into that a few times myself. Also, I read somewhere that you have to put the path to the file you want to extract too. If I backup /home and then want to extract /home/dale/Desktop then it would be -f /home/dale/Desktop for tar to find the file. If -z doesn't help, try checking the path. Maybe it needs that.
Hope that helps.