Here are some questions to ask yourself:
Why did the character change?  Why did the character see things differently at the end of the story than she or he did in the beginning?  What events or people moved the character to his or her new life or attitude? 

What are the most important influences in that person's life?   Who were her friends?  What are their goals and aspirations?  Did any of these things change? 

Examine the changes a character goes through in the book.  Characters learn how to cope, build themselves up to a challenge, or conquer a serious flaw within themselves.  Often a character's self-esteem is built up during the story.  Look at the changes your character goes through.  If you believe that the character has changed, then you can show that this happened by comparing how the character did things in the novel's beginning and how much better (or worse) the character handled things at the novel's end.  Psychoanalyze the character. 

Gaining Maturity
Growth of Ponyboy in A.E. Hinton's The Outsiders

In the novel The Outsiders, Ponyboy makes the passage from a maladjusted teen to a young adult ready to undertake the serious tasks of life.  The novel begins with Ponyboy running away after his friend kills another boy.  Ponyboy cannot relate to his older brother, who represents authority to him.  As the story goes on, Ponyboy learns quite a bit, but the reader sees that he is still not ready to enter the adult world when in the book's middle he enters into a gang fight.  Ponyboy doesn't change until the death of his friend Johnny.  Johnny's death makes Ponyboy realize the seriousness of life.  After that, even if he does not always agree with his older brother, Ponyboy is finally is able to understand the view of the world the way his brother sees it.  The novel ends with Ponyboy knuckling down to undertake what is required of him at school, on the road to achievement instead of running away from his responsibilities.