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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.
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.
* 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.
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.
equation of the tangent linexa a=t is given by y=f(a)+-f¢(a)(xa). 2. fa¢( ) is the instantaneous rate of change of fx( ) at xa= . 3. If fx( ) is the position of an object at time x then fa¢( ) is the velocity of the object axat = . Basic Properties and Formulas
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.
