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AP Calculus AB Exam Prep
Math Facts for the AP exam
79
Mathematics
12th Grade
03/24/2010
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Intermediate Value Theorem
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If f(x) is continuous on the closed interval [a,b], then for any k between f(a) and f(b), there exists c between a and b, such that f(c)=k.
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Limit Definition of the derivative
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The limit as h approaches 0 of

(f(x+h)-f(x))/h

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ln 1
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0
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∫x-1 dx
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ln |x| + C
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∫(1/(1+x2) dx
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tan-1x + C
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The conditions for the Mean Value Theorem
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f(x) must be continuous on the closed interval [a,b] and differentiable on the open interval (a,b).
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The conclusion of the Mean Value Theorem
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There exists c in (a,b) such that f'(c) = (f(b)-f(a))/(b-a)
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The average value of a function on an interval [a,b].
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The average rate of change of a function, f(x), on an interval [a,b].
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ZERO!
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Intermediate Value Theorem
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If f(x) is continuous on the closed interval [a,b], then for any k between f(a) and f(b), there exists c between a and b, such that f(c)=k.
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The average rate of change of a function, f(x), on an interval [a,b].
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