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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.
Effortlessly memorize all the AP® Calculus BC formulas using our clear and organized Formula and Equation Sheet, specially made for your prep!
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.
A function y = f (x ) is even if f ( − x ) = f ( x ) for every x in the function’s domain. Every even function is symmetric about the y-axis. A function y = f (x ) is odd if f ( − x ) = − f ( x ) for every x in the function’s domain. Every odd function is symmetric about the origin. 3.
AP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore ...
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.
b − a. ____________________________________________________________________________________ Rolle's Theorem: If f is continuous on [ a , b ] and differentiable on ( a , b ) and if. f ( a ) = f ( b ) , then there exists a number c on ( a , b ) such that f ' ( c ) = 0.
