Question Which of the following statements are true and which are false? I. An absolute maximum of a function \( f(x) \) is the largest value of all the \( y \)-values of \( f(x) \) (on the entire domain of \( f(x) \) ). II. A function can have more than one absolute maximum. III. A local maximum \( f(c) \) of a function \( f(x) \) is the largest of all \( y Which of the following statements are true and which are false? I. An absolute maximum of a function \( f(x) \) is the largest value of all the \( y \)-values of \( f(x) \) (on the entire domain of \( f(x) \) ). II. A function can have more than one absolute maximum. III. A local maximum \( f(c) \) of a function \( f(x) \) is the largest of all \( y \)-values of \( f(x) \) when \( x \) is near \( c \) on both sides (specifically, on some open interval containing \( c \) ). IV. A function can have more than one local maximum. V. A function can not have both a local and an absolute maximum at the same point \( c \). \( \mathrm{VI} \). It is possible for a function to have \( \mathrm{NO} \) absolute maximum and \( \mathrm{NO} \) absolute minimum. VII. If a function is CONTINUOUS on a CLOSED BOUNDED interval, then the function is guaranteed to have an absolute maximum and an absolute minimum. VIII. The Extreme Value Theorem (Theorem 4.1) says that only continuous functions have an absolute maximum and an absolute minimum on every closed bounded interval.

For x∈[−12,11] the function f is defined by f(x)=x7(x+4)2 On which two intervals is the function increasing (enter intervals in ascending order)? ___to___ and ___ to___

The number of students infected with the flu on a college campus after t days is modeled by the function 200 What is the maximum number of infected students possible The number of students infected with the flu on a college campus after days is modeled by the function P 1.19-23 OA 120 students Ostudents C 4 stores OD 240 students

Please show all work, thank you! Find the solution space of the homogeneous system of equations. X1 -3x2 + x3=0 2x1 - 6x2 +2x3=0 3x1 -9x2 + 3x3=0

Moments and shear stress 2. The following figure shows all the stresses on a small volume element (of volume dxdydz) in equilibrium. By calculating the moments about the centre of the element and understanding that in equilibrium the total sum of moments around the x, y and z axes are zero, prove that: Txy Tyx Txz = T7x and Tyz Tzy dx буг бу dz Ох бу Оух xy Moments and shear stress 2. The following figure shows all the stresses on a small volume element (of volume dxdydz) in equilibrium. By calculating the moments about the centre of the element and understanding that in equilibrium the total sum of moments around the x, y and z axes are zero, prove that: Txy Tyx Txz = T7x and Tyz Tzy dx буг бу dz Ох бу Оух xy бх dy (Hint: calculate the moments about the centre of the element in the x, y and z axes separately.) 60

7–26. Lagrange multipliers Each function ƒ has an absolute maximum value and absolute minimum value subject to the given constraint. Use Lagrange multipliers to find these values. ƒ(x,y) = x2 subject to x2 + xy + y2 = 3

The Gourmand Cooking School runs short cooking courses at its small campus. Management has identified two cost drivers it uses in its budgeting and performance reports—the number of courses and the total number of students. For example, the school might run two courses in a month and have a total of 65 students enrolled in those two courses. Data concerning the company's cost formulas appear below: Instructor wages Classroom supplies Utilities Campus rent Insurance Administrative expenses Fixed Cost per Cost per Cost per Month Course Student $ 2,960 $280 $1,240 S 80 $4,600 $2,400 $3,600 44 S 5 $ For example, administrative expenses should be $3,600 per month plus $44 per course plus $5 per student. The company's sales should average $890 per student. The company planned to run four courses with a total of 65 students; however, it actually ran four courses with a total of only 57 students. The actual operating results for September appear below: Revenue Instructor wages Classroom supplies Utilities Campus rent Insurance Administrative expenses Actual $ 54,950 $11,120 $ 18,050 $ 1,970 $ 4,600 $ 2,540 $ 3,527 Required: Prepare a flexible budget performance report that shows both revenue and spending variances and activity variances for September. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.) Required: Prepare a flexible budget performance report that shows both revenue and spending variances and activity variances for September. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.) Gourmand Cooking School Flexible Budget Performance Report For the Month Ended September 30 Flexible Actual Results Budget Planning Budget Courses 4 Students 57 $ 54,950 Revenue Expenses: Instructor wages Classroom supplies Utilities Campus rent Insurance Administrative expenses Total expense Net operating income 11,120 18,050 1,970 4,600 2,540 3,527 41,807 13,143 $