Here's why:
* Infinitive: The infinitive form of a verb is "to" + the base form of the verb (e.g., "to devote").
* Infinitive Phrase: An infinitive phrase includes the infinitive and any objects or modifiers that go with it. In this case, "to devote" is the infinitive, and "to her painting" is the object of the infinitive.
The phrase "to devote to her painting" functions as an adjective modifying the noun "time". It tells us what kind of time Frances has.