In literature climax is the point in a plot that creates the greatest intensity, suspense, or interest. The climax is usually the point at which the conflict in the story is resolved. So, the reader must not make a subjective judgment in determining climax, but, rather look closely at the sequence of events and find the particular event that is the turning point with regard to the conflict.
The conflict of the very poignant story "The Last Leaf" by O. Henry involves Sue's loving attempts to keep her friend Johnsy from her determination to perish from pneumonia: the doctor tells Sue, "Your little lady has made up her mind that she's not going to get well." And, in her efforts to prevent Johnsy from dying when the last leaf of the vine outside the window dies, Sue tells Johnsy she must close her eyes while she uses the light from the window to paint by, using Old Behrman as a model. Sue goes downstairs to Behrman and tells him of her fears that Johnsy, fragile as a leaf herself, may float away as her hold upon the world grows weaker.
After Sue paints with Behrman modeling as an old miner, she finds Johnsy staring at the shade. When Sue raises the shade for her friend, they find one tenacious leaf hanging from a branch above them. Despite another storm, the leaf is yet there the next morning. Here, then, is the climax:
Johnsy lay for a long time looking at it. And then she called to Sue, who was stirring her chicken broth over the gas stove.
"I've been a bad girl, Sudie," said Johnsy. "Something has made that last leaf stay there to show me how wicked I was. It is a sin to die. You may bring me a little broth now, and some milk with a little port in it, and--no, bring me, a hand-mirror first, and then pack some pillows about me, and I will sit up and watch you cook."
After this speech by Johnsy, the conflict is resolved, and the falling action brings the reader to the surprising conclusion of Mr. Behrman's sacrifice--his masterpiece--to save the life of Johnsy.
In my opinion, the climax of this story comes when Johnsy decides that she is going to live. This comes after she sees the "leaf" still there on the second day and she starts to talk to Sue about what she thinks it means.
The conflict in this story has been, in my opinion, between Johnsy and herself. She is having to decide if she wants to live. At the point in the story that I mention, she says that she has decided that it was wrong of her to want to die and that she will try to live. This resolves the conflict of this story.