This is a take home test I need to do thanks.

Exam 4 Chapter 12 take home portion Name___________________ David Hallberg Instructor. And remember no WORK means NO credit! MATH-115-A and B Give exact values when possible or round to five decimal places. (Use separate sheets for work; List only the solutions on this sheet) Due Monday December 1st , 2014 at the start of class 1) A rectangular beam will be cut from a cylindrical log of circumference of 60 inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log. Note: k is a constant. ANSWER__________________ 2) Find a cubic function f ( x) ax3 bx 2 cx d that has a local maximum value of 60 at x= 1 and a local minimum value of 4 at x= 3 . ANSWER__________________ 3) A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 32 ft, find the dimensions of the window so that the greatest possible amount of light is admitted. ANSWER__________________ 4) A rectangular field is to be enclosed on all four sides with stone edging. The stone edging material costs $6 per foot for the two sides that contain the width of the enclosed area and $8 dollars for the two sides that contain the length of the enclosed area. Find the maximum area that can be enclosed for $4000? a) Construct a picture of the situation with proper labels. b) Find the maximum area. ANSWER__________________ 5) In statistics the normal curve, given by ( ) ( ) the mean and the standard deviation have specific roles. The mean is the center of the curve. Show that the Hergert number is one standard deviation away from the mean [answer ] Students may not receive any assistance from a tutor or instructor on this take home exam! However Students who form study groups will receive 5 bonus points. Groups are limited to five students and you must meet together for at least an hour. This is repeatable to 15 points also three of the group members must be new to that group each time. You are required to list each group member on each person's exam for each study group. Graph each function: It must be hand drawn on graph paper it will take a whole sheet of paper for each graph and list the relevant information You are to find each and plot on the graph if applicable Domain: Symmetry Even Odd Neither: x-intercept(s): y-intercept: Vertical Asymptote(s): Horizontal Asymptote(s): Slant Asymptote(s): Removable Discontinuity(s): End Behavior the limits as x approaches infinity or negative infinity: First Derivative and Critical Point(s): Maximums and Minimums Points also stat if global min or global max: Second Derivative Hergert number and Candidates for Inflection Point(s): Second Derivative Test to Classify the Critical Point: Explain any unique aspects of your function (keep it brief) Your problems are 3 6) f (x ) x x 2 7) f (x ) ln x 2 2x 2 8)f (x ) 1 1 e x Bonus f (x ) 1 x 1 x2 2 1 x3 32 x4 4 32 x5 5 4 32 x6 65 4 32 ... This is a polynomial representation of an elementary function what is the function? And what processes did you use to determine the function. Students may not receive any assistance from a tutor or instructor on this take home exam! However Students who form study groups will receive 5 bonus points. Groups are limited to five students and you must meet together for at least an hour. This is repeatable to 15 points also three of the group members must be new to that group each time. You are required to list each group member on each person's exam for each study group