MTH 105 Lecture Notes - Lecture 2: Trigonometric Functions, Maxima And Minima, Piecewise

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plummoose320

28 Mar 2017

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Provide a generalization to each of the key terms listed in this section. When functions are increasing, decreasing, or constant from its own graph. When it"s on an open interval, i, if, for any possible choice of both x1 and x2 in i when noting that x1 < x2, which therefore notes that f (x1) < f (x2) When it"s on an open interval, i, if, for any possible choice of both x1 and x2 in i when noting that x1 < x2, which therefore notes that f (x1) > f (x2) When it"s on an open interval, i, if, for any possible choice of just x in i when the values in f (x) are all equal. What"s the di erence between a maximum and minimum: maximum. The maximum would be the largest y-value for any function: minimum. The minimum would be the smallest y-value for any function.

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If U and V are positive constants, find all critical points of the function. (Enter your answers as a comma-separated list.) F(t) = Ue t + Ve -t t = Find all critical points of f(x) = 20 x 2 e - 0.3x and classify them as local minima of ,maxima. x = (smaller value) This critical point is a . x = (larger value) This critical point is a . Consider f(x) = x 8 (7 - x) 9. Find f '(x) and simplify your answer. f '(x) = Find all critical points of f(x) and then use the first derivation test to determine local maxima and minima. f(x) has a at x = (smallest value) Local Maximum OR Minimum OR Neither f(x) has a at x = Local Maximum OR Minimum OR Neither f(x) has a at x = (largest value) Local Maximum OR Minimum OR Neither Find the inflection points of f(t) = t 4 + t 3 - 18t 2 +8. Give exact answer. t = (smallest value) t = (largest value) Sketch a possible of y = f(x), using the given information about derivation y' = f'(x) and y" = f"(x). Assume that the function is defined and continuous for all real x. Let f be a function f(x) > 0 for all x. Let g = 1/f. If f is increasing in an interval around x 0, what about g? g is increasing in an interval x 0. g is zero in an interval around x 0. g is decreasing in an interval around x 0. We cannot tell whether g is increasing or decreasing in an interval around x 0. g is constant in an interval around x 0. If f has a local maximum at x 1, what about g? g has a local maximum at x 1. g has both a local minimum and a local maximum at x 1. We cannot tell whether g has a local minimum or a local maximum at x 1. g has an inflection point at x 1. g has a local minimum at x 1. If f is a concave down at x 2, what about g? g is increasing at x 2. g is flat at x 2. We cannot tell whether g is concave up of concave down at x 2. g is concave down at x 2. g is concave up at x 2. You are given the graph of the second derivation function f" below. Which of the given have x-values that are inflection points of the function f? (Select all the apply.) A B C D E F G H I none of the above

MTH 105 Lecture Notes - Lecture 2: Trigonometric Functions, Maxima And Minima, Piecewise

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