Theoroms
If a function is continuous on a closed interval [a,b ] and f(a) ( ), then for every value of between ( ) and ( ), there exist at least one value of in the open interval ( ) so that ( ) .
The
If a function is continuous on a closed interval [ ], then: 1. There exists a number in [ ] such that ( ) ( ) for all in [ ]. 2. There exists a number in [ ] such that ( ) ( ) for all in [ ].
The Extreme Value Theorem(EVT)
If a function is continuous on a closed interval [ ], differentiable on the open interval ( ), and ( ) ( ), then there exists a number in the open interval ( ) such that ( ) .
Rolles Theorem