Answer:
C) to show that Derek succeeded in using the Dream Machine to complete his project
Step-by-step explanation:
So, the previous paragraphs established the problem of the story; Derek has a project that is due tomorrow, he hasn't even started writing it, he has no idea what to write and his brother presents him with the possible solution - the Dream Machine.
Now, the paragraph 8 shows the way machine works, paragraph 9 shows that the machine works and that in his dream he saw the Olympics - the theme of his project, and paragraph 10 shows his teacher praising him for the job he had done on the project.
These three paragraphs imply that Derek successfully used the Dream Machine which helped him complete his project.