1. The speaker can extemporize on any of a number of subjects.
2. I'd lost my notes and had to extemporize.
3. He has to extemporize because he has forgotten to bring his note.
4. He had to extemporize because he had forgotten to bring his notes.
5. Certain performers can extemporize.
6. The actress forgot her lines and had to extemporize.