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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.
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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.
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,
* 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.
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Page 1 of 2. Mathematics document from Northern Virginia Community College, 2 pages, AP ® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this website. AP® Calculus BC - Formula Sheet Identities to Recall sin (−θ) = − sin (θ) cos (−θ) = cos (θ) tan (−θ) = − tan (θ ...
