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Let f be defined at c. If f c 0 or if f is undefined at c, then c is a critical number of f. _______________________________________________________________________ First Derivative Test: Let c be a critical number of a function f that is continuous on an open interval I containing c.
b a ______________________________________________________________________________ Intermediate Value Theorem: If f is continuous on [a, b] and k is any number between f (a) and f (b), then there is at least one number c between a and b such that f (c) = k.
Formulas for AP Calculus BC Update 2023 NameFormulas for AP Calculus. slope of a parametrized curve. ∫ tanu du. ∫ cotu du=: ∫ secu du=: ∫ cscu du=: Integration by parts. o.rder for choosing u in integration by parts: logistics differential equation.
Source: adapted from notes by Nancy Stephenson, presented by Joe Milliet at TCU AP Calculus Institute, July 2005 CALCULUS BC ONLY Integration by Parts: ∫ ∫ u dv uv v du = −
The AP Calculus BC Formula Sheet is a reference sheet provided to students during the AP Calculus BC exam. It contains key formulas and concepts that students are expected to know and apply in solving problems.
First Fundamental Theorem of Calculus: b c a ³ f x dx f b f a Second Fundamental Theorem of Calculus: x a d f t dt f x dx ³ Chain Rule Version: d gx ³ a f t dt f g x g x dx c _____ Average value of f (x) on [a, b]: 1 b AVE a f f x dx ba ³
Calculus BC Formulas. Section 1: Limits. Intermediate Value Theorem (IVT) If a function ƒ is continuous on the interval [a, b] and k is a number between ƒ(a) and ƒ(b), then there is at least one x-value c between a and b such that ƒ(c) = k. y. ƒ(b) ƒ(a) < k < ƒ(b) k. c. 2. ƒ(a) a. c. 3. x. b < c < b. Any continuous function connecting (a,
