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Rolle's Theorem
Assume f(x) is a function which satisfies all of the following.
1. f(x) is continuous in the closed interval [a,b].
2. f(x) is differentiable in the open interval (a,b).
3. f(a) = f(b)
So, there is a number c as a < c < b and f′(c) = 0. Or, though f(x) has a critical point in (a,b).
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Properties of Dot Product u → • (v → + w → ) = u → • v → + u → • w → (cv → ) • w → = v → •(cw → ) = c (v → •w → ) v → • w → = w → • v →
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Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
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