Comments:

- (Section F) For the first problem, we need the mean value theorem precisely. Any proof based on intuition but didn’t rely on the mean value theorem will lose points.
- (Section G) For the first problem, most of the students wrote that since the mean value theorem doesn’t give us a contradiction. However, that doesn’t directly tell us the it is possible to find such a function. The direct proof is to see that the linear function f(x)=\frac{31}{9}+\frac{5}{9}x satisfies the conditions.