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7 Cards in this Set

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Intermediate Value Theorem
Let f(x) be continuous on the interval (a,b). If K is any number between f(a) and f(b) then there is at least one number c in (a,b) such that f(c)=K
The Extreme Value Theorem
If f(x) is continuous on (a,b) then f(x) has both a global maximum and a global minimum at points in (a,b).
Local Extrema Test
If f(x) is defined on an interval and if f(x) has either a local maximum or a local minimum at a point c which is not an endpoint of the interval, then either f'(c)=0 or f'(c) does not exist.
The Differntialbility-Continuity Thm
If f'(c) exists, then f(x) is continuous at x=c.
Mean Value Thm
If f(x) is continuous on (a,b) and differntiable on (a,b) then there exists a number c, with a<c<b such that if f'(c)=(f(b)-f(a))/(b-a)
Constant Functio Thm:
If f(x) is continuous on (a,b) aand if f'(x)=0 on (a,b), then f(x) is constant on (a,b).
Fundamental Theorem of Calculus
If f(x) is continuous on (a,b) and if F(x) is an antiderivative for f(x), then
integral a to b f(x)dx=F(b)-F(a)