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Extreme Value Theorem

If a function is continuous on the closed interval [a.b] it must have both a maximum and minimum on the interval

Intermediate Value Theorem

If a function is continuous on the closed interval [a,b] and u is a value between f(a) and f(b), there exists a point x=c such that f(c)=u

Rolle's Theorem

If f is continuous on [a,b] and is differentiable on (a,b) and f(a)=f(b), then there exists a c such that f'(c)=0

Mean Value Theorem

If f is continuous on [a,b] and is differentiable on (a,b) then there exists a c such that f'(c)=[f(b)-f(a)]/(b-a)