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MATH-M 119 Lecture Notes - Lecture 3: Fixed Cost, Marginal Cost, Variable Cost

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27 Aug 2018

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MATH-M 119 Lecture 2: Interpretations of Derivatives Part 2

MATH-M 119 Lecture Notes - Lecture 3: Fixed Cost, Marginal Cost, Variable Cost

MATH-M 119 Lecture Notes - Lecture 12: Microsoft Powerpoint, Dependent And Independent Variables

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V(t): represents value of an item as a function of time t. Example: a new bus worth ,000 in 2010 depreciates linearly to ,000 in 2030. T= # of years since 2010 (0, 100000) (20, 20,000) What are the horizontal and vertical intercepts and what do they represent? (0, 100000) = vertical value at t= 0 (25, 0) = horizontal value at y=0. Cost, revenue, and profit: p: price per item, q: quantity (# items produced) The cost function c(q) gives the total cost of producing some goods. Cost of raw materials = per widget. Revenue function r(q) gives the total revenue received from selling a quantity q of some good. If the price is a constant, then the revenue function is a linear function of q. profit function. The breakeven point is the point where the profit = 0 and the revenue = cost. breakeven point: When q changes by +1 ----> selling one more item.

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Answer question numbers #6,#12,#14,#16,#20 include full steps and solutions with explation of your answers.

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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

question 23 please