A toy train runs back and forth down a linear track. Its position is given during selected times as it moves along the track. t (minutes) P(t) Position in meters 5 8 12 15 40 80 60 20 45 (59) P(0) : (60) P(8) – P(2)
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- Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate of change of y = √(4 - x2) on the interval [ - 2, 2]. Explain how this can happen.An investor has his savings invested in various investments. The amount at the end of each month, in the first semester, is shown in the table. a. Assuming that the rate of change of the amount can be represented by: y ′ (x) = (0.06y (x)) / x, obtain an approximation for the amount in the month of August, using the Improved Euler method, using h = 1 and initial condition given by the data for the month of June.b. What is the relative percentage error knowing that the particular solution of the PVI is y (x) = e ^ (0.06 lnx + 4.46).Find the average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to 5
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- Write a plot of a Gaussian function with x-axis range from -3 to +3 and y-axis range from 0 to 1.2The success of a project depends on the effort level of a worker. In case of successthe revenues will be 400,000 TL whereas in case of no-success the revenues will be 0. The workercan provide a low effort level or a high effort level. The effort level cannot be observed by theprincipal. The worker requires an expected salary of 60,000 TL to provide the low effort leveland an expected salary of 80,000 TL to provide the high effort level. The success probabilitiesfor the project are 40% in case of low effort level and 80% in case of high effort level. Whatshould be the minimum bonus (that is awarded in addition to the base salary in case of success)and the base salary for the worker so that the worker has the incentives to provide the higheffort level?An orchard has an average yield of 36 bushels of apples/tree if the density is 22 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels/tree. How many trees per acre should be planted in order to maximize the total yield? Justify your answer using the extreme value theorem or global first or second derivative test.