Αποτελέσματα Αναζήτησης
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.
* If x-values are NOT evenly divided the formulas for Riemann Sums and Trapezoidal Rule do NOT apply! Use the intervals given on the table provided for ∆𝒙.
Mean Value & Rolle’s Theorem. If the function f(x) is continuous on [a, b] and the first derivative exists on the interval (a, b), then there exists a number x = c on (a, b) such. ) − f ( a )that f '( c ) =b . if f(a) = f(b), then f ’(c) = 0.
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.
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,
