The words contained in this file might help you see if this file matches what you are looking for:

...Mean value theorem meanvalue if you averaged miles per hour during a trip then at some instant the were traveling exactly that relatively obvious statement is as it applies to particular may seem strange such simple would be important or useful anyone but and of its consequences are very in variety areas many results rest this chapter depend on one corollaries will used every time we calculate an integral later chapters truly delightful aspect mathematics idea can so powerful before state prove examine someofits consider simplied version called rolle s pick any two points x axis think about all differ entiable functions pass through those because our differentiable they must continuous their graphs cannot have holes breaks also since these dif ferentiable derivatives dened everywhere between not corners vertical tangents margin gure still sorts shapes unlikely common properties other than ones stated michel found he noticed has more where tangent line horizontal see result named after ...