'Kavirajamarga', the earliest available work on poetics in the Kannada language, was written by (or in the court of):

"Kavirajamarga" ("The Royal Path for Poets"), the earliest available work in the Kannada language, was written by (or under the patronage of) the Rashtrakuta king Amoghavarsha I, in the 9th century CE.

About Kavirajamarga:

• It was composed around 850 CE.
• It is a work on poetics (alankara, the theory of poetry), describing the rules of composing poetry in Kannada.
• It is based partly on an earlier Sanskrit work on poetics.
• Many scholars believe that it was actually written by the court poet Shri Vijaya (Srivijaya), under the patronage of Amoghavarsha I.
• It describes the Kannada-speaking region as extending from the Kaveri to the Godavari, and praises the Kannada people as skilled in poetry.
• It is important for the history of the Kannada language and literature.

About Amoghavarsha I:

• He ruled from about 814 to 878 CE, for more than 60 years, one of the longest reigns in Indian history.
• He was the son of Govinda III.
• He was a peaceful ruler, more interested in religion, literature and culture than in war.
• He built the city of Manyakheta (Malkhed) as his capital.
• He was a patron of Jainism, and his teacher was the Jain scholar Jinasena, author of the "Adipurana".
• He also wrote a Sanskrit work, "Prashnottara Ratnamalika" ("Garland of Gems of Questions and Answers"), which was later translated into Tibetan.
• The Arab traveller Sulaiman described him as one of the four greatest kings of the world.

Scholars at his court:

• Jinasena: Adipurana.
• Mahaviracharya: the mathematician who wrote "Ganitasarasangraha".
• Shakatayana: the grammarian who wrote "Amoghavritti".

Kannada literature:

• The three great early Kannada poets (the "three gems", Ratnatraya) were Pampa, Ponna and Ranna (10th century).
• Kannada was declared a classical language in 2008.

Why not the other options?

• ✗Pulakeshin II, Vishnuvardhana and Krishnadeva Raya were other rulers.