The author's purpose simply means the reasons an author has for writing a selection or a poem.
Your information is incomplete. Therefore, an overview will be given. Authors may have more than one purpose for writing. The purpose of a poem can be stated explicitly or readers may have to infer the intent.
The mood of the poem is the atmosphere of the poem, and the tone is the poet's attitude towards the topic. They can identify by looking at the setting, characters, details, and word choices. These are important in knowing the purpose or theme of the poem.
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