MATH 1505 Midterm: Worksheet mock test Feb 14_2013.pdf

Document1 Word Akbar, Hi Mailings Review View Tell me what you want to do 三三물 :ー,'e! .田. |TNormal INO Spac Heading 1 Heading 2 Title Subtitle Subtle Em- Paragraph Styles Finds all critical points Use the second derivative test to classify the critical points as local maxima or local minima ifthe test Find the intervals on which the function is increasing and on which the function is decreasing. fails, say so). Find the intervals on which the function is concave up and on which the function is concave down. Determine all points of inflection. Using ONLY the information from the previous steps (DO NOT GRAPH ON YOUR CALCULATOR!!!I, sketch an accurate graph of the function. Be sure to plot all points of inflection as well as local maximums and local minimums.

In Problems 1-4, find all critical points and determine whether they are relative maxima, relative minima, or horizontal points of inflection. 17. Given y 6400x 18xnd the absolute maximum and minimum for y when (a) 0x 50 and (b) 0 s xS 100. In Problems 18 and 19, use the graphs to find the following items. (a) vertical asymptotes (b) horizontal asymptotes (e) lim (d lim) 18 3, f(x) = 1-3x + 3x2-x3 f(x) = +1 In Problems 5-10: (a) Find all critical values, including those at which f(x) is undefined. (b) Find the relative maxima and minima, if any exist. (c) Find the horizontal points of inflection, if any exist. (d) Sketch the graph. y = f(x) d a 6, f(x) = 4x3-x" -2 15 8. y = 5x7-7x5-1 9, y=x2/3-1 10, y = x2/3(x-4)2 19. 11. Is the graph ofy = x4-3x3 + 2x-1 concave up or concave down at x = 2? 2. Find intervals on which the graph ofy = x4-2x3 12x + 6 is concave up and intervals on which it is concave down, and find points of inflection. 13. Find the relative maxima, relative minima, and points 9x+ 10. of inflection of the graph of yx in Problems 14 and 15, find any relative maxima, relative In Problems 20 and 14 n, and points of inflection, and sketch each graph. In Problems 20 an 15, y=2+5x3-3x5 16, Given R and any vertical asymptotes. 3x + 2 2x 21, y = 280x-x, find the absolute maximum ) 0 s x S 200 and and minimum for R when (a (b) 0 x 100