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7 Cards in this Set
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 Back
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 DifferntialbilityContinuity 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))/(ba)


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) 