וַיֹּ֤אמֶר אֱלֹהִים֙ אֶל־יוֹנָ֔ה הַהֵיטֵ֥ב חָרָֽה־לְךָ֖ עַל־הַקִּֽיקָי֑וֹן וַיֹּ֕אמֶר הֵיטֵ֥ב חָֽרָה־לִ֖י עַד־מָֽוֶת׃
И сказал Бог Ионе: 'Ты сильно сердишься на тыкву?' И сказал он: 'Я очень зол, даже до смерти.'
Ibn Ezra
investigate well here means intensely (as in “I am greatly angry” [Jonah 4: 9]). The word well is closely related to the Hebrew word for “good”.
From David to Destruction
Sefer Yonah ends with a dramatic flair. After Nineveh repents from its evil ways, Yonah travels in anger to the outskirts of the city and waits to see what will happen to it. There, Hashem designates a Kikayon (a leafy plant, see Rashi ad loc.) to provide shade for Yonah. The Navi is elated. However, Hashem then sends a worm to destroy the plant. Once again exposed to the elements, Yonah feels faint and asks for death. At this point, Hashem asks Yonah, “HaHeiteiv Charah Lecha Al HaKikayon,” “Are you so deeply grieved over the Kikayon?,” to which Yonah responds, “Heiteiv Charah Li Ad Mavet,” “I am greatly grieved to death” (Yonah 4:9).