Answers to math 230

1. The slope of a function at the point of its local or global maxima is zero. Explain why using an example. The slope of a function is zero at the point of its local or global maxima because of the fact that it is the point where the function is horizontal, thus the slope is really zero. For example, given a function f(x) =-x^2. The first derivative of f is -2x and equating it to zero will yield to solution x=0 which is our candidate for maximum or minimum point. Furthermore, we apply the second derivative test. The second derivative is -2 thus 0 is a local maximum. Accidentally 0 is the only local maximum thus 0 is also the global maximum of the function. At x=0, f(x) =0, which has slope of 0. 2. Show how the derivative of the function f(x) = (2x^4) (3x+2)2 can be obtained with out using the product rule. We can differentiate the given function 2x^4 (3x+2)2 without using the product rule by just simply distributing (2x^4) to the term (3x+2) giving you 6x^5+ 4x^4. Afterwards, multiply it with the constant 2, thus you have 12x^5+8x^5. Now you can solve the derivative using the simple idea of getting the derivative of function.   Hence you have (12)(5)(x^5-1)+(8)(5)(x^4-1) yielding you to 60x^4+40x^3 which is the derivative of the function f. 3. Provide a discussion showing that the limit of the function, f(x) =2x^4 / (x-2) does not exist at x=2. It is possible that the limit of a given function doest not exist at a particular point. In the problem, to show that the limit of f(x) as x approaches 2 does not exist we need to get the right hand side and left hand side limit of f(x). The right hand side limit of f is positive infinity while the left hand side limit of f is negative infinity. Since they are not equal, we are forced to conclude that the limit of f(x) does not exist. Reference: What the Derivative Tells Us About a Function. Retrieved October 12 2007 from http://www.ugrad.math.ubc.ca/coursedoc/math102/keshet.notes/chapter5

Productivity Essay Example | Topics and Well Written Essays - 2000 words

Productivity - Essay Example define productivity as a measure of performance as compared to the ratio of output produced in relation to the input inserted into any task or project. This definition, however, shouldn’t tie any other opinion down as various knowledge bases would come up with various definitions given their respective contexts. Many factors have been brought to the forefront in a bid to expound the basis that productivity is defined. Leonhard and Simaan consider productivity as a function derived from quality of work, time, and the initial budget. On the other hand, Young groups factors that affect productivity such as the human resource management, work environment, and the particular job in context (Young, 2010). This report will consider some of those factors that affect productivity, especially in construction-related projects, therefore, trying to see points in which productivity could be improved. The structure of the paper will have a literature review section, an analysis of the relevant aspects that surround productivity, and a conclusion summed up from the entire work (Leonhard and Simaan, 2010). This section will sample two case studies of construction projects where analyses were performed to measure the productivity levels at each scenario using various techniques, and the conclusion summed up from the analyses. The undertaken steps to rectify the factors that lowered productivity will be discussed. All these discussions will be aligned with the factors that affect productivity and the refinement will help us see some ways to improve productivity; these aspects will be expounded more in the next section of this report. Construction of the Commercial Bank Headquarters in Edinburgh was undertaken as a case study to see some of the factors that affected productivity. The managers in charge of this big project took the initiative to check up on their employee productivity. The main participants were the top-level project managers and the onsite workers who were used

California Pacific Medical Center Research Paper

California Pacific Medical Center - Research Paper Example †¢ Ownership: CPMC is owned by Sutter West Bay Hospitals in San Francisco. It is a private company that comes under the category of medical centers. At present Mr. Martin Brotman is the Managing Director cum President of these institutions. The top management of these hospitals consists of other five members also. †¢ Population served: Being a not-for-profit health system, the CPMC serves tens of thousands of patients and their families in cities and towns of Northern California. The doctors, health care service providers and hospitals of this institution connect resources and allocate know-how to improve the health care quality of the population over here. †¢ Accreditation received: For the services rendered by it, the Leapfrog group has recognized it as one of the top hospital in the country for safety and quality in the year 2010. The US News and World Report accepted the CPMC as one of the best hospitals that treat gastrointestinal disorders in the year 2008. In 2007, four neurosurgeons in CPMC received the Physician Recognition Award from the National Committee for Quality Assurance. In the same year, the hospital was also accredited with VHA West Coast Performance along with other five hospitals. In 2006, the Joint Commission certified CPMC as a Primary Stroke Centre for the commitment to excellence in stroke management. In the very same year it also received the recognitions like Accreditation by Society of Chest Pain Centers and United Health Premium Cardiac Specialty Designation. Users of health information Doctors and nurses: Each year the doctors and nurses of this institution learn more about what the patients expect fr om them. This also helps to teach the coming generation about the health care facilities provided by CPMC. Administrators: Administrators are informed about the changes taken place in the field of health care so that decisions can be taken in order to keep up to date with the changes. Support services: Support services use health information whenever they are called for assistance by any third party or the patient himself. External users: The health information will be helpful to outsiders in knowing how their health will be protected. Each time they visit a doctor, the hospital records it. This record contains a description of the