At what point is the tension highest in the book Old man and the sea? How has the author built this tension? Does it lead to the climax?

Hemingway's The Old Man and the Sea is a complexly constructed story that gradually develops to a climax. The tension starts to build at the very beginning of the story when the reader is introduced to Santiago. Hemingway builds sympathy for Santiago and introduces the main dramatic conflict of the story, namely his poverty and struggle to catch a fish. Through the interactions of Santiago and the boy, readers see how Santiago's pride struggles with his run of bad luck and growing physical incapacity while at the same time showing him as a mentor and father figure, increasing readers' sympathy with him and our hope that he will manage to catch a fish rather than having to rely on charity and suffer from poverty and a loss of his identity as a skilled fisherman. Thus Hemingway starts building a sense of tension as readers empathize with Santiago's struggles.
When Santiago takes his boat out, the tension builds more, in part because the climax is delayed. Rather than just quickly telling readers about Santiago's skill and understanding of the sea, instead Hemingway shows readers how Santiago uses deep knowledge of the behavior of local wildlife and knowledge of the area to search for fish and involves the reader in the details of the fishing. Readers also get to see Santiago's deep love for and harmony with the ocean and its denizens and his simple piety, building our degree of empathy for Santiago. This increases the tension in the story as readers are hoping for an encounter with a big fish and empathizing with Santiago as the encounter is delayed.
Finally, as Santiago finds the marlin and struggles to kill it, the tension is at its highest point. The description of Santiago injuring his hand and his increasing tiredness and pain ratchets up the level of tension in the story as well as making the outcome doubtful. Santiago is struggling as much with his own frailty as with the fish, and in both cases the struggle is one that is nuanced. He admires the fish and is almost reluctant to kill it, but needs to do so. The tension builds as the fish and Santiago both weaken, and is at its greatest just before Santiago kills the fish in the climactic three paragraphs beginning:

He took all his pain and what was left of his strength and his long gone pride and he put it against the fish's agony and the fish came over onto his side and swam gently on his side, his bill almost touching the planking of the skiff [...].