Song He hurriedly examined the problem. It was a very conventional major problem, probably modified from the final major problem of the gaokao.
This kind of problem was very difficult for ordinary students, but it was nothing to Song He. After looking at it for a few seconds, a string of steps popped into his mind, and before he knew it, he had mentally calculated the final answer.
"Can you find the monotonicity in the first part?" Song He asked.
"Yes." Zhuang Qiyan nodded. "I can't do the second part."
"For the second part, I'll teach you a conventional method and a separation of variables method. The conventional method is troublesome, while separation of variables is simpler, but you need to practice it." Song He said.
Zhuang Qiyan hurriedly took the paper and pen, adopting an attitude of eager attention, looking just like a well-behaved student humbly seeking guidance from her teacher.
"For the conventional method, first set g(x) equal to f(x). Pay attention to the range of x. That's one point right there." Song He picked up his pen and rapidly wrote on the scratch paper. "Then take the derivative once to get g', and again to get g''. At this point, it's monotonically decreasing from 0 to ln3 and monotonically increasing from ln3 to positive infinity. That's another point..."
Zhuang Qiyan hurriedly followed along, jotting things down on the scratch paper with her pen, her eyes tense.
Song He filled a large sheet of paper with elegant writing, discussing two different cases and proceeding step by step. He had even marked the score for each step, ultimately arriving at a dazzlingly complicated result.
"Do you understand this conventional method?" Song He turned his head.
Zhuang Qiyan rested her chin on her hand in thought, lightly biting her lip.