Every infinitive consists of the root of a verb plus the word "to" (called an "infinitive particle"). You should remind yourself as often as you can that the infinitive particle "to" is a must for all infinitives: it's how an infinitive is identified. Remember that the preposition "to" is an altogether different word, and that it's followed by an object noun (or noun-like words), whereas the infinitive particle "to" is always followed by a base form of a verb: "to dock the ship" instead of "bring the ship to the dock."
Some other important reminders about infinitives:
When an infinitive or an infinitive phrase is used to describe "Which?," "What kind?," "How?" and "When?" it's acting just as a modifier would. Below are some examples of how infinitives and infinitive phrases are used as adjectives and adverb. (For more information about how they are used as nouns, see "Nouns: Noun-Type Verbals: Infinitives.")
The way to identify if an infinitive is behaving as an adjective is to determine whether it answers the adjective questions "Which? or "What's it like?" because, if an adjective modifies a noun, then an infinitive phrase behaving as an adjective must also modify one or more of these in a sentence:
There are two infinitives in the sentence above. Only one of them is an adjective. First, the verb in the main clause, "leads," is causative: one action causes another by way of an indirect object. If "many species" is the indirect object, then the infinitive phrase "to migrate large distances" is the direct object. By nature, all objects are nouns or words acting like nouns, so, in this case, "to migrate" is a noun infinitive. The remaining infinitive, "to produce offspring in a safe environment" answers the question "Which urge?" The answer is "The urge to reproduce," so this infinitive and its predicate object are all part of a single adjective infinitive phrase.
Because an infinitive adjective phrase doesn't need to go on a horizontal line, it doesn't use the "raised platform" method that infinitive noun phrases use. Instead, they are placed under the nouns they modify, connected by diagonal lines the way other modifiers are. Your first instinct will be to say that "many species" is the direct object and "to migrate large distances" answers the question "How does it lead them." And you'd be right. The causative verbs can be thought of in this way as well, but, again, it's merely convention that they must be rendered with indirect objects and prepositional phrases as direct objects. Another way to think of the infinitive phrase "to migrate large distances" is that it answers the question, "What are many species lead to do?" Phrased this way, we expect the answer to be a noun, and that's what we get:
Adverb infinitives are the most difficult to classify, even though they're not difficult to recognize. This is because the common adverb has, not one, but three modifying functions. It can modify verbs, as in "walks further"; it can modify adjectives, as in "takes a slightly inconvenient route"; and it can modify other adverbs, as in "walks even further." The way to identify if an infinitive is behaving as an adverb is to determine if, in the sentence, it answers the adverb questions "How?", "How much?" or "When?"
The infinitive phrase, "to prevent their own depression and burnout" answers the question "Struggle how?" "Struggle" is an intransitive verb, so a word modifying a verb is always going to be an adverb. The infinitive "to prevent" is derived, not from an intransitive verb, but a transitive one, so it takes a predicate object, "depression and burnout." The entire infinitive phrase, then, modifies the verb "struggle" and is therefore adverbial.
The infinitive phrase, "to make difficult life-and-death decisions" answers the question "Forced how?" "Forced" is a past participle modifying "E.R. physician." A past participle is a kind of adjective, so a word modifying an adjective is always going to be an adverb. The infinitive "to make" clearly modifies an adjective and is therefore an adverbial infinitive phrase.
For a change, the rules for diagramming an adverbial infinitive modifying an adjective are simple and intuitive. No, really. Just extend a zig-zag line from the diagonal line containing the adjective, and "hang" the infinitive phrase from it as you would a bird- feeder. Then, sit back and enjoy whatever wisdom the birds start bringing.
Just as an adverb modifying an adverb is far less common, an adverbial infinitive modifying an adverb is less common, but it happens enough to warrant mention. In fact, the sentence I just wrote contains an adverbial infinitive phrase modifying an adverb: "it happens enough to warrant mention." The word "enough" is an adverb modifying "happens," and "to warrant mention" modifies the degree of "enough." Any word modifying an adverb must, itself, be an adverb, so an infinitive phrase modifying one must be an adverbial infinitive. Here's another example:
As can be seen from the example, the infinitive phrase "to make any real difference" follows on the heels of the adverb "sufficiently." It answers the question "How sufficiently?" which is typical of most adverbs modifying other adverbs: they describe degree or intensity. Words like "more," "less," "enough," "adequately" and, yes, "sufficiently" are the most commonly occurring of these.
The rules for diagramming an adverbial infinitive phrase that modifies an adverb are virtually no different from those governing an adverbial infinitive modifying an adjective.