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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.
Calculus BC Review Sheet LIMITS lim ... FUNDAMENTAL THEOREM OF CALCULUS Part 1 1 If ( T) is continuous on [a, b] and 𝐹( T) is the anti-derivative of ( T), then ... * 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.
c. If f is differentiable on the interval, except possibly at c, then f c can be classified as follows. 1) If f x changes from negative to positive at c, then f c is a relative minimum of f. 2) If f x changes from positive to negative at c, then f c is a relative maximum of f.
23 Σεπ 2024 · Download the AP Calculus BC Cheat Sheet (Free PDF) for unit-wise formulas, key concepts, and examples, designed to enhance your exam prep and boost your score.
Differentiation Formulas Basic Integral Formulas Cracking the AP Calculus AB Exam 2017, Premium Edition Princeton Review (Firm),David Kahn,2016-08 Readers will find proven techniques for a higher score on these exams Includes five full
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.
Calculus Formulas. d + 1. Power Rules: x n = nx n − 1 xn and ∫ xn dx = + c dx n + 1. d. Product Rule: [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ g ' ( x ) + f ' ( x ) ⋅ g ( x ) dx. d ⎡ f x ⎤ g x f ' x f x ⋅ g ' x. Quotient Rule: ( ) ( ) ⋅ ( ) − ( ) ( ) dx ⎢ = ⎣ g ( ) x ⎥ ⎦ [ ( g x ) ]2.