Mean Value Theorem

My favorite theorems ever are the main concepts in this section!

Rolle’s Theorem, named after the French mathematician Michel Rolle (1652–1719), gives conditions that guarantee the existence of an extreme value in the interior of a closed interval. These conditions are that the functions must be continuous on a closed interval and differentiable on that same interval (only open) while both endpoints of the interval have the same y-values. When this occurs, there is at least one number such that the derivative at that point is equal to zero. Fun!

Mean Value Theorem is related, but has different conditions. These conditions are that the functions must be continuous on a closed interval and differentiable on that same interval (only open) while both endpoints of the interval can have the different y-values. When this occurs, there is at least one point such that the derivative at that point is equal to the slope of the endpoints. Super fun!