What is the first appearance of the F-bomb in a movie?

Contentious.

Most sources claim Robert Altmans MASH* contained the first 'Fuck' in a major motion picture, it was already the first for other things (first use of sound bridging!) so it's happy to push boundaries. It was actually only the first Hollywood film to do so.

That being said, the climax of The Graduate (1967) features a scene in which Ben Braddock can be seen (but not heard) shouting "What the fuck are you doing?" to Elaine as she stands at the alter, as he is behind glass.

However, both Ulysses and I'll Never Forget What's'isname used it beforehand, both also being released in 1967. Ulysses however, was released in June of that year as opposed to the December opening of I'll Never Forget What's'isname, making Ulysses the winner.

1967 was a good 'fucking' year.

Others have argued over the first 'profanity' spoken in a movie, with Hell's Angels being the most likely candidate (considering the amount of times 'damn' and 'son-of-a-bitch' is apparently uttered during dogfight sequences).

You can hear Tony Curtis mutter "fucked up" in THE BOSTON STRANGLER (1968), first use in an American major studio film I know of. It's translated that way in the cc, also.

"The Mystery of Mr. Wong" (1939), a Boris Karloff "James Lee Wong" serial entry. A man has just been found slugged unconscious. The police and PI Wong are already on the scene. A party of house guests comes in and one of them, approaching, asks, "Street! Wong! What the fuck just happened?"

I listened to it over and over. It's there. Movie is available on Amazon Prime. I gather, given the production values, there was probably little or no money for retakes. (Not a BAD flick, but not a lavish production.)

First word fuck appeared in movies in 1963.

see video proof

As you can see in the video, first F word film is Vapors (1963).

In "55 days at Peking" about 2 hrs and 20 min in an off screen voice uses the f word in haranguing his men to put out fires with buckets. This was 1963.

It was an intentional use of the word in two Warner Bros. films, both in 1933. Bosko, the cartoon, pretty clearly says, "The dirty fuck!" in Bosko's Picture Show.

The movie Gold Diggers of 1933 has character actor Guy Kibbee sitting down talking to Warren William. Kibbee reminisces about a love he had some years back. He said, "She always called me Fucky...I don't know why, but she called me Fucky. Even if he was saying Vucky or Vuckie, with no hard emphasis on the V, it would sound like Fucky". And it did.

Warners always pressed the envelope in the face of what they could get by with, after all there was not yet a real censorship office set up until the following year.

It was used by James Caan near the finale of LADY IN A CAGE (1964).