Homework 6

Page 1 of 6 MATH 2413 Calculus I WRITTE N HOMEWORK ASSIG N ME N T 6 MAI N REVIEW SHEET FOR TEST 2 PART 2 Selected problems from Chapter 3 N ame: ________________________________ PSID: _________________________________________ Instructions: • Print out this file (or download and work directly on your tablet / laptop) and complete the problems. If the problem is from the text, the section number and problem number are in parentheses. You must submit your work in this format to get credit. • If you choose not to print the homework file and wish to use your own paper, you must copy the problem and set up your pages to follow the same structure of the homework file. Your submission should be an exact replica of the online file (in terms of pages and questions on each page). • Use a blue or black pen or a pencil (dark) and write neatly. Do not use any red pen(s). • Write your work in the space provided and your solutions in the boxes provided. You must show all your work in order to receive credit for a problem. The graders are looking for proper notation, good logic, and correct answers. Neat and organized work is important for full credit. • Your work is to be uploaded into CA N VAS before the posted date and time. It should be submitted as a SI N GLE PDF file, not pictures, not separate files, not a word doc. Follow the instructions given on CANVAS to upload the file and click on the submit button. After submitting, check that you have submitted a single PDF file successfully, and all pages are readable. If the grader can’t read your work, the problem will not be graded. It is your responsibility to check that the file is saved in the system and is complete. • Late work cannot be submitted in lab or via email. Only uploaded ON TIME homework will be graded. Please plan ahead. • Students are expected to adhere to the UH Academic Honesty Policy. Submitting someone else’s work is considered a violation of this policy. Unless otherwise stated, calculators or other software are not allowed. Sign Below to Promise that you will follow UH Academic Honesty Policy: Signature: __________________________________________________________________ Emily Drilling 1941 852 Eleg

Page 2 of 6 1. Given ࠵? is defined on all real numbers and ࠵? ′′ (࠵?) = 10(࠵? + 4)(࠵? + 2)(࠵? − 5) 2 ; find the interval(s) over which the function is concave down. Determine the x-coordinates of any points of inflection. 2. Determine the critical points and identify any vertical tangents or cusps. (a) ࠵?(࠵?) = (࠵? − 5) 4 7 ⁄ (b) ࠵?(࠵?) = (࠵? 2 + ࠵?) 3 5 ⁄ ( - 1 - )(+ ) W - W ~ ! i I - x + ) t + ( + 1 + ) - S I I st + (4)( + ( - 5 - 4 - 3 - 88 D concave down at : 1-0 , -4) and 1-2 , 00 40I : x = - 4 x = - 2 f(x) = Exx - 5) 51x ⊥ X = 5 [ vertical crsp ex = 5] f(x) = E(x2 + x) - = . (ex + 1) Et -ex + 1) x = - 42 93 5(x2 +x) = X = 0 X = - 1 vertical tangent & X = - 1 , 0

Page 4 of 6 5. Given a function and its derivatives: ࠵?(࠵?) = 5࠵? (࠵?−1) 2 ; ࠵? ′ (࠵?) = −5࠵?−5 (࠵?−1) 3 ; ࠵? ′′ (࠵?) = 10࠵?+20 (࠵?−1) 4 . (a) Write the domain of this function: _____________________________ (b) Write down the horizontal asymptotes (if any): _____________________________ (c) Write down the vertical asymptotes (if any): _______________________________ (d) Write down any intercepts (as points): _______________________________ (e) Find the critical points; classify them. Write down the intervals of increase/decrease. (f) Write down the intervals of concave up/down. Write down the x-coordinates of any points of inflection. Use the information you have found to graph this function. Clearly LABEL the intercepts, any extreme points, any points of inflection on the graph. Include the asymptotes. ( - 0 , 1)( , ) H . A . = y = 1 V . A = x = 1 i0 , is = / - I only - 5x - 5 = 0 increase of (-1 , 17 - W - 5x = 5 decrease &2 ! x = - 1 (-0 , - 1)(1 , 0) 10 x + 20 = 0 - st Poze(-2 , -1019) 10x = - 20 x = = 2 x = 1 concave down (-cs , -2) concave up e(-2 , d) ! I I I I - -- - - - - & POl I I I local ⑳ min I

Page 5 of 6 6. Given ࠵?(࠵?) = ࠵? 2 (࠵?−4) 2 and its derivatives ࠵? ′ (࠵?) = −8࠵? (࠵?−4) 3 , ࠵? ′′ (x) = 16࠵?+32 (࠵?−4) 4 . Find the domain, asymptotes, critical numbers, relative extrema, intervals of increase/decrease, concavity, and graph the function. Be sure to mark the relative extrema and points of inflection on the graph. domain : ( - , 4)(4 , 1) asymptotes : U . A . @X= 4 H . A . 2 X = 1 ⊥ CN = x = 0 - I - local min & (0 , 0) Hi decreasing of < - - , 0(d( - - c) - 10245 increasing & (8 , 4) S W v concave up & (2 , a) Eit concave down & <-as , -2) I I I I I ~ - -- - - - - i