1. When both choices are given, we generally use whether rather than if:
- I don't know whether she's coming or not. (It would be possible to use if here, but less common.)
2. Before an infinitive with to we use whether:
- I don't know whether to accept their offer or not. (If would not be used here.)
3. We can use whether after a preposition:
- It's a question of whether we can agree on everything. (If would not be used here.)
4. Both whether and if can be used in indirect speech to introduce a yes/no question:
- Did they say whether/if they were going to be late?
5. After some verbs, we use whether:
- I doubt whether they'll make it.
- We discussed whether it was the correct decision.
Google.com results: Of whether | Of if | Whether to | If to
Dictionary.com definitions: Whether | If