Is the mean value theorem for integrals the same as the mean value thoerem for derivatives?

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

Which expression is equivalent to -12(3x-3/4)