When do we use the words credible, creditable and credulous?

These words all derive from the Latin verb 'credere', meaning 'to believe or entrust'.

Credible and credulous both have the notion of believing, but in different ways. 

CREDIBLE means 'believable' or 'reliable':

• A credible account of the event, credible alibi, credible act.

Credible is also used in extended sense, 'authentic, convincing, sound' :

• She doesn't seem to be a credible candidate for this post.
• She makes a credible mother.

The opposite of credible is incredible, means only 'unbelievable' and, informally, 'wonderful, marvelous':

• an incredible performance.

CREDULOUS is used exclusively of humans and human behaviour, never for things. 

It is applied to people who are, as it were, on the receiving end of a credible story, and means 'believing too readily, gullible':

• She is a credulous naivete.
• A credulous simpleton.

There are also signs of stupendous naivety-Feigenbaum and McCorduck, for example, are limitlessly credulous about the ability of the Japanese to achieve their immoderate objective.

-John Naughton, The Observer.

The opposite of credulous is incredulous which means the opposite, 'disbelieving, sceptical' or 'expressing disbelief'.

The feeling persisted for long when in front of her incredulous eyes he enacted a drama of betrayal.

CREDITABLE,finally, has lost its connection with the notion of disbelief, believing, and means 'worthy of credit, deserving praise and admiration':

• His creditable attempt to save the clan was appreciated.
• The companies were on cloud nine after their creditable collaboration.

Polk-Mowbray threw himself into the arrangements with great abandon....It promised to be the most original party of the year...All in all it was most creditable to those concerned.

-Antrobus, in Lawrence Durrell's Esprit de Corps.