Calc Theorems

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AP Calc AB Theorems

Calculus

Calc Theorems

IVT

FTC

AP Calc AB

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7 Terms

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Extreme Value Theorem

If f is continuous on a closed interval [a,b], then f has both an absolute minimum and absolute maximum

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Intermediate Value Theorem

If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there is at least one value c in the closed interval [a,b] such that f(c) = k

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Mean Value Theorem

If f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a value c in (a,b) such that…

<p>If f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a value c in (a,b) such that…</p>
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Rolle’s Theorem

  • Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b)

  • If f(a) = f(b), then there is at least one value c in (a,b) such that f ' (c) = 0

<ul><li><p>Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b)</p></li><li><p>If f(a) = f(b), then there is at least one value c in (a,b) such that f ' (c) = 0</p></li></ul>
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The Fundamental Theorem of Calculus

If f(x) is continuous and integrable on [a,b] and F(x) is the antiderivative of f(x) then…

<p>If f(x) is continuous and integrable on [a,b] and F(x) is the antiderivative of f(x) then…</p>
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FTC Part 2

If f is continuous on the open interval I containing a, then for every x in I

<p>If f is continuous on the open interval I containing a, then for every x in I </p>
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Extension of FTC Part 2

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