The man page did not clearly specify this. But looking at openssl's apps implementations, SSL_CTX_use_PrivateKey* calls are usually made after SSL_CTX_use_certificate_file succeeded. I assume this is mostly used at the server side.
I recently confused the above function with SSL_CTX_load_verify_locations wherein you could specify a CA certificate file and path. It turned out that SSL_CTX_load_verify_locations is the one I needed to verify a server certificate which is signed by a Trusted Authority.