2/28/2017 Sections 11.5 - 12.2 Dustin Kelly MTH 217, section 22318443, Spring 2017 Instructor: Daniel Sievewright WebAssign Sections 11.5 12.2 (Homework) Current Score : - / 81 Due : Thursday, March 2 2017 12:10 PM EST 1. -/1 pointsWaneFMAC6 11.5.002. Find the derivative of the function. f(x) = ln(x + 1) f '(x) = 2. -/1 pointsWaneFMAC6 11.5.007. Find the derivative of the function. h(x) = ex + 5 h'(x) = 3. -/1 pointsWaneFMAC6 11.5.012. Find the derivative of the function. g(x) = 4x g'(x) = https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 1/16 2/28/2017 Sections 11.5 - 12.2 4. -/1 pointsWaneFMAC6 11.5.034. Find the derivative of the function. HINT [See Example 1a.] s(x) = ln (x 7)2 s'(x) = 5. -/1 pointsWaneFMAC6 11.5.046. Find the derivative of the function. f(x) = 6ex x2ex f '(x) = 6. -/2 pointsWaneFMAC6 11.5.090. The average price of a twobedroom apartment in the uptown area of a prominent American city during the real estate boom from 1994 to 2004 can be approximated by p(t) = 0.15e0.10t million dollars (0 t 10) where t is time in years (t = 0 represents 1994). What was the average price of a twobedroom apartment in this uptown area in 2002, and how fast was it increasing? (Round your answers to two significant digits.) HINT [See Quick Example 3.] p(8) = $ million p'(8) = $ million per yr https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 2/16 2/28/2017 Sections 11.5 - 12.2 7. -/3 pointsWaneFMAC6 11.5.104. An epidemic follows the curve 800 million people 1 + 20,000e0.549t where t is in years. How fast is the epidemic growing after 10 years? (Round your answer to two P = significant digits.) HINT [See Example 5.] million people infected per year How fast is the epidemic growing after 20 years? (Round your answer to two significant digits.) million people infected per year How fast is the epidemic growing after 30 years? (Round your answer to two significant digits.) million people infected per year 8. -/3 pointsWaneFMAC6 11.6.005. Find dy/dx, using implicit differentiation. HINT [See Example 1.] 4x + 9y = xy dy = dx Compare your answer with the result obtained by first solving for y as a function of x and then taking the derivative. y= dy = dx https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 3/16 2/28/2017 Sections 11.5 - 12.2 9. -/1 pointsWaneFMAC6 11.6.012. Find the indicated derivative using implicit differentiation. HINT [See Example 1.] 2x2 y2 = 3 dy dx dy = dx 10.-/4 pointsWaneFMAC6 11.6.054. The number of cellphone accessory kits (neon lights, matching covers, and earpods) per day that USA Cellular Makeover Inc. can manufacture at its plant in Cambodia is given by P = x0.5y0.5 where x is the number of workers at the plant and y is the monthly budget (in dollars). Assume P is dy constant, and compute when x = 500 and y = 200,000. HINT [See Example 5.] dx dy = $ per worker dx Interpret the result. The monthly budget to maintain production at the fixed level P is Select $ by approximately per additional worker at an employment level of 500 workers and a monthly operating budget of $200,000. In other words, increasing the workforce by one worker will result in a savings of approximately $ per month. https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 4/16 2/28/2017 Sections 11.5 - 12.2 11.-/8 pointsWaneFMAC6 12.1.002. Locate and classify all extrema in the graph. (By classifying the extrema, we mean listing whether each extremum is a relative or absolute maximum or minimum.) Also, locate any stationary points that are not relative extrema. HINT [See figure.] (Order your answers from smallest to largest x.) (x, y) = f has Select at . (x, y) = f has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 5/16 2/28/2017 Sections 11.5 - 12.2 (x, y) = f has Select at . (x, y) = f has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 6/16 2/28/2017 Sections 11.5 - 12.2 12.-/6 pointsWaneFMAC6 12.1.006. Locate and classify all extrema in the graph. (By classifying the extrema, we mean listing whether each extremum is a relative or absolute maximum or minimum.) Also, locate any stationary points that are not relative extrema. HINT [See figure.] (Order your answers from smallest to largest x.) (x, y) = f has Select at . (x, y) = f has Select at . (x, y) = f has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 7/16 2/28/2017 Sections 11.5 - 12.2 https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 8/16 2/28/2017 Sections 11.5 - 12.2 13.-/6 pointsWaneFMAC6 12.1.011. Locate and classify all extrema in the graph. (By classifying the extrema, we mean listing whether each extremum is a relative or absolute maximum or minimum.) Also, locate any stationary points that are not relative extrema. HINT [See figure.] (Order your answers from smallest to largest x.) (x, y) = f has Select at . (x, y) = f has Select at . (x, y) = f has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 9/16 2/28/2017 Sections 11.5 - 12.2 14.-/8 pointsWaneFMAC6 12.1.015. Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.] (Order your answers from smallest to largest x.) g(x) = 2x3 24x with domain [4, 4] (x, y) = g has Select at . (x, y) = g has Select at . (x, y) = g has Select at . (x, y) = g has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 10/16 2/28/2017 Sections 11.5 - 12.2 15.-/4 pointsWaneFMAC6 12.1.022. Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.] (Order your answers from smallest to largest x.) f(x) = 3x4 2x3 with domain [1, +) (x, y) = f has Select at . (x, y) = f has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 11/16 2/28/2017 Sections 11.5 - 12.2 16.-/6 pointsWaneFMAC6 12.1.025. Find the exact location of all the relative and absolute extrema of the function. HINT [See Examples 1 and 3.] (Order your answers from smallest to largest x.) h(x) = 5(x 1)2/3 with domain [0, 2] (x, y) = h has Select at . (x, y) = h has Select at . (x, y) = h has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 12/16 2/28/2017 Sections 11.5 - 12.2 17.-/6 pointsWaneFMAC6 12.1.028. Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.] (Order your answers from smallest to largest x.) k(x) = 2x (x 1)2/5 with domain [0, +) 5 (x, k) = k has Select at . (x, k) = k has Select at . (x, k) = k has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 13/16 2/28/2017 Sections 11.5 - 12.2 18.-/2 pointsWaneFMAC6 12.1.034. Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.] (Order your answers from smallest to largest x.) g(x) = 23 23 2 x x (x, y) = g has Select at . 19.-/6 pointsWaneFMAC6 12.1.039. Find the exact location of all the relative and absolute extrema of the function. HINT [See Example 1.] g(t) = et t with domain [1, 1] (t, y) = g has Select at . (t, y) = g has Select at . (t, y) = g has Select at . https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 14/16 2/28/2017 Sections 11.5 - 12.2 20.-/2 pointsWaneFMAC6 12.2.009. For a rectangle with a perimeter 20 to have the largest area, what dimensions should it have? (Enter the smaller value first.) 21.-/2 pointsWaneFMAC6 12.2.011. Assume that it costs Apple approximately C(x) = 36,100 + 100x + 0.01x2 dollars to manufacture x 32GB iPods in a day. How many iPods should be manufactured in order to minimize average cost? iPods per day What is the resulting average cost of an iPod? (Give your answer to the nearest dollar.) HINT [See Example 1.] $ 22.-/3 pointsWaneFMAC6 12.2.040. A company manufactures cylindrical metal drums with open tops with a volume of 2 cubic meters. The metal used to manufacture the cans costs $2 per square meter for the sides and $3 per square meter for the (thicker) bottom. What should be the dimensions of the drums in order to minimize the cost of metal in their production? HINT [See Example 4.] (Round the radius to four decimal places, and round the height to three decimal places.) radius height m m What is the ratio height/radius? (Round your answer to one decimal place.) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 15/16 2/28/2017 Sections 11.5 - 12.2 23.-/1 pointsWaneFMAC6 12.2.063. Your automobile assembly plant has a CobbDouglas production function given by q = x0.4y0.6, where q is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $20,000 per employee plus the operating budget of $365y. Assume that you wish to produce 2,000 automobiles per year at a minimum cost. How many employees should you hire? HINT [See Example 5.] (Round your answer to the nearest employee.) x = employees 24.-/3 pointsWaneFMAC6 12.2.030. In the 1930s a prominent economist devised the following demand function for corn: p = 6,640,000 , q1.3 where q is the number of bushels of corn that could be sold at p dollars per bushel in one year. Assume that at least 6,000 bushels of corn per year must be sold. (a) How much should farmers charge per bushel of corn to maximize annual revenue? HINT [See Example 3, and don't neglect endpoints.] (Round to the nearest cent.) p = $ (b) How much corn can farmers sell per year at that price? q = bushels per year (c) What will be the farmers' resulting revenue? (Round to the nearest cent.) $ per year https://www.webassign.net/web/Student/Assignment-Responses/last?dep=15844770 16/16