Password: final Final Exam Using Proctorio https://www.desmos.com/scientific  

What is the primary goal of Six Sigma?

During the chronic inflammation stage, the goals of healing are:

Instructions:  On a separate sheet of paper, answer each of the exam problems shown below. Write your answers clearly. Unless otherwise stated, you will need to justify your answers to get the full credit. Problem 1. (10 pts)  Consider the function f(x1,x2)=2x1x2+1+x2{“version”:”1.1″,”math”:”f(x_1, x_2) = \frac{2x_1}{x_2+1} + x_2 “} and the point x(0)=⊤{“version”:”1.1″,”math”:”\( x^{(0)}=\left^{\top}\)”}. Construct (5 pts) a linear approximation, l(x1,x2){“version”:”1.1″,”math”:”\( l(x_1, x_2)\)”}, of f(x1,x2){“version”:”1.1″,”math”:”\(f(x_1, x_2)\)”} at x(0){“version”:”1.1″,”math”:”\( x^{(0)}\)”}; (5 pts) a quadratic approximation, q(x1,x2){“version”:”1.1″,”math”:”\( q(x_1, x_2) \)”}, of f(x1,x2){“version”:”1.1″,”math”:”\(f(x_1, x_2)\)”} at x(0){“version”:”1.1″,”math”:”\( x^{(0)}\)”}.   Problem 2. (10 pts)  Is d=⊤{“version”:”1.1″,”math”:”\( d=\left^{\top}\)”} a direction of ascent of f(x1,x2)=2x1x2+1+x2{“version”:”1.1″,”math”:”f(x_1, x_2)=\frac{2x_1}{x_2+1} + x_2 “} at the point x(0)=⊤{“version”:”1.1″,”math”:”\( x^{(0)}=\left^{\top}\)”} or not? Justify your answer. If yes, then why? If not, then why not?   Problem 3. (10 pts)  Consider the function f(x)=(Ax)⊤(Bx),{“version”:”1.1″,”math”:” f(x)=(A x)^{\top}(B x), “} where A={“version”:”1.1″,”math”:”\( A=\left\)”}, B={“version”:”1.1″,”math”:”\( B=\left\)”} , and x=⊤{“version”:”1.1″,”math”:”\( x=\left^\top\)”}. (5 pts) Find ∇f(x){“version”:”1.1″,”math”:”\( \nabla f(x)\)”}. (5 pts) Find the Hessian F(x){“version”:”1.1″,”math”:”\( F( x)\)”} of f(x){“version”:”1.1″,”math”:”\(f(x)\)”}.     Problem 4. (20 pts)  Given the following function, f=f(x1,x2)=ex2cos⁡x1−ex1cos⁡x2.{“version”:”1.1″,”math”:”f=f(x_1,x_2)=e^{x_2}\cos x_1-e^{x_1}\cos x_2. “} (10 pts) In what direction does the function f{“version”:”1.1″,”math”:”\( f\)”} increase most rapidly at the point x(0)=⊤{“version”:”1.1″,”math”:”\( x^{(0)}=\left^{\top}\)”}? (10 pts) What is the rate of increase of f{“version”:”1.1″,”math”:”\(f \)”} at the point x(0){“version”:”1.1″,”math”:”\( x^{(0)}\)”} in the direction of maximum increase of f{“version”:”1.1″,”math”:”\(f\)”}?   Problem 5. (15 pts)  (5 pts) Find the factor by which the uncertainty range is reduced when using the Fibonacci method. Assume that the last step has the form 1−ρN−1=F2F3=23,{“version”:”1.1″,”math”:”1-\rho_{N-1}=\frac{F_2}{F_3}=\frac{2}{3}, “} where N−1{“version”:”1.1″,”math”:”\( N-1\)”} is the number of steps performed in the uncertainty range reduction process. (10 pts) It is known that the minimizer of a certain unimodal function f(x){“version”:”1.1″,”math”:”\( f(x)\)”} is located in the interval {“version”:”1.1″,”math”:”\(\left\)”}. What is the minimal number of iterations of the Fibonacci method required to box in the minimizer within the range 1.0{“version”:”1.1″,”math”:”\(1.0\)”}? Assume that the last useful value of the factor reducing the uncertainty range is 2/3{“version”:”1.1″,”math”:”\( 2/3\)”}, that is, 1−ρN−1=F2F3=23.{“version”:”1.1″,”math”:”1-\rho_{N-1}=\frac{F_2}{F_3}=\frac{2}{3}. “}   Problem 6. (15 pts)  minimize‖x+x0‖2subject tox=1,{“version”:”1.1″,”math”:”\begin{eqnarray*} \mbox{minimize}&{}& \|x+x_0\|_2\\ \mbox{subject to}&{}&{}\\ {}&{}& \leftx=1, \end{eqnarray*}”} where x0=⊤.{“version”:”1.1″,”math”:”x_0=\left^{\top}. “} Problem 7. (20 pts)  (10 pts) Convert the optimization problem, minimize|x1|+|x2|+|x3|subject to=,{“version”:”1.1″,”math”:”\begin{eqnarray*} \mbox{minimize}&{}& |x_1|+|x_2|+|x_3|\\ \mbox{subject to}&{}& {}\\ &{}& \left\left=\left, \end{eqnarray*}”} into a linear programming problem and solve it. Hint: Introduce two sets of non-negative variables:    xi+≥0{“version”:”1.1″,”math”:”\(x_i^+\ge 0\)”}  and xi−≥0,{“version”:”1.1″,”math”:”\( x_i^- \ge 0, \) “} i=1,2,3.{“version”:”1.1″,”math”:”\( i=1,2,3. \)”} Then represent the optimization problem using the above variables. Only one xi+{“version”:”1.1″,”math”:”\( x_i^+ \)”} and xi−{“version”:”1.1″,”math”:”\( x_i^- \)”} can be non-zero at a time. If  xi≥0{“version”:”1.1″,”math”:”\( x_i \ge 0 \)”} then xi=xi+{“version”:”1.1″,”math”:”\( x_i=x_i^+ \)”} and xi−=0.{“version”:”1.1″,”math”:”\( x_i^- =0. \)”} On the other hand, if xi

Restrictions in passive range of motion include all of the following EXCEPT:

What does the Control phase ensure in Six Sigma?

Which of the following best describes the social development of children in middle childhood? 

A rigid state in which the person has hypertonicity in the neck and back extensors; the hip extensors, adductors, and internal rotators; the knee extensors; and the ankle plantarflexors and invertors, and with the elbows are held rigidly at the sides, with wrists and fingers flexed, but with elbows extended describes:

All of the following are physiologic effects of thermotherapy EXCEPT:

Which is NOT a cardinal sign of inflammation?