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- How are the absolute maximum and minimum similar to and different from the local extrema?4. An analyst has found that Granny's Surf Board Company monthly profit function is: P(x) =- 0.05x2 +50x - 2000, where x is the number of boards produced and sold. Determine the maximum profit function and number of items needed produce and sell reach the maximum profit. Graph the results with Desmos or by hand. first derivative critical numbers stationary points 3. ャーナーキーナー+ー I I I IIII III I I L Lーム 3. I II 1 III .L L -L-L-1Differentiate. 4) f(x) = e2x 5) y = e6x2, x
- 1) Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.3. (Sections 4.1 and 4.3) READ CAREFULLY. The graph of y f'(x) is given. %3D (a) Use the graph to find the critical numbers of f. Explain how you found your answer(s). (b) Use the First Derivative Test to classify each of the critical numbers as locations of local maximum values of f, local minimum values of f, or neither. Give reasons for your answers. S(x). (c) ): Use your work above to sketch a possible graph of y Dfind all the critical values (if any) of y=x square-root (x-2)(1-x)
- A patient is given a drip feed containing aparticular chemical and its concentration inhis blood is measured at half hour intervals.A linear relationship exists between the variables such that for any given time the concentration is given in the table below. (i) Develop a model that predict the concentration of chemical mentioned aboveas drip keeps feeding the chemical oversome time. (3)Differentiate.9. Find the values of x that give relative extrema for the function h(x) = 3x5 – 5x3 A. Relative maximum: x = -1 ; Relative minimum: x = 1 3 B. Relative maximum: x = 0; Relative minimum: x = C. Relative maximum: x +1;Relative minimum: x = 0 D. Relative maximum: x = 0; Relative minimum: x = ±1 %3D
- 2) A production function for a business follows the model P(L, K) = 0.1 L0.4K0.6 over the course of one year, where P represents the total value of all products the company makes, L represents the value of the labor from employees, and K represents the value of all the company's assets (buildings, machines, etc.), where everything is measured in millions of dollars. ap a. Find and ƏL ap ак' , and explain what they represent in this context. b. Evaluate the partial derivatives from part a when (L, K) = (3,4). If this was your business and your values, if you wanted to expand would it be better to expand in workforce (increase L) or expand in assets (increase K)?The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)4. Final: A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain between 15 95 ounces and 16.05 ounces. A jai is selected from the process every half hour until a sample of 100 jars is obtained When the fills of the jars are measured, it is found that x (xbar) = 16.0024 ands = .02454. Using x (xbar) and s as point estimates of u (meu) and a (sigma). estimate the probability that a randomly selected jar will have a fill, x, and that is less than minimum reading Assume that the process is in contiol and that the population of all jar fills is normally distributed. O a. .0391 O b. .0411 O c.0229 O d. .0166 O e. None of the above 1) HUAWEI