Number of Local Extrema Graph the polynomial, and determine how many local maxima and minima it has. 63. y = -2x? + 3x + 5 64. y = x' + 12x -65. y = x - x - x -67. y =x - 5x + 4 66. y = 6x + 3x + 1
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- Application of Differential Calculus: Optimization Farmers use a certain plant food costing $4.00 per ounce to help them in growing oranges. It is estimated that when x ounces of the food are used on an ace of orange grove, the farmer is able to get Ln(4x+5) crates of oranges from that acre of land. If the farmer can sell the oranges at $20 per crate, how many ounces should be used per acre to maximize the orange crops net value.POLYNOMIAN AND RATIONAL FUNCTIONSSeveral popular models of carry-on luggage have a length 10 in greater than their depth to comply with airline regulations, the sum of the length, width, and depth may not exceed 40 in. What is the maximum possible volume of a piece of luggage? What are the corresponding dimensions of the luggage? Look for the greatest value of y that occurs within the domain 0, x, 15.Application of derivative Optimization We are going to fence in a rectangular field that encloses 200 m2. If the cost of the material for of one pair of parallel sides is $3/m and cost of the material for the other pair of parallel sides is $8/m determine the dimensions of the field that will minimize the cost to build the fence around the field.
- The long run. A chair manufacturer hires its assembly-line labour for $18 an hour and calculates that the rental cost of its machinery is $6 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. The firm is currently using 1 hour of labour for every 3 hours of machine time. (Assume that labour is on the horizontal axis and capital is on the vertical axis). 3. Graphically illustrate your answer by drawing an isoquant, an isocost line for the current combination of labour and capital and an isocost line for the optimal combination of labour and capital. An isocost corresponding to the optimal combination of labour and capital is [a vertical line, a horizontal line, an upward sloping straight line, an upward sloping curve which is not a straight line, a downward sloping straight line, a downward sloping curve which is not a straight line, L-shaped] has slope [ ] at the optimal combination of inputs An isoquant…th degree polynomial function with rea n=3;3 and i are zeros; f(2)=25Dynamic profit function is P(t)= 2 - (t - 5) x ln (t + 1), here t is measured in years, and P is measured in hundreds of euros. a) use marginal analysis to estimate how fast company's profit was growing initially b) use Taylor formula to write down square approximation of the given profit function around t=2. Round coefficient of the Taylor polynomial to 3 decimals c) use results from step b) to estimate total company's profits between first and fourth years of operation d) estimate average company's profit between first and fourth years of operation e) use initial function to estimate total company's profits between first and fourth years of operation. Compare results with step c) the question is not graded, as the exam was yesterday, I want to check my answers
- numerical solution B. Find the interpolating polynomial of the following point and function using Lagrange interpolation process.1. (-3,0), (-1,2), (0,-2), (1,3) and (3,-1). 2. y = cos ( 2x ) at x = [0,π] with four equally spaced points.Volume The measured volume of a pyramid with eachedge of the base equal to x units and with its altitude(height) equal to x units is given in the table below.a. Determine whether the second differences of theoutputs are constant.b. If the answer is yes, find the quadratic model thatis the best fit for the data. Otherwise, find thepower function that is the best fit.1.Identify the kind of function. 2.Find the x- and y- intercepts and the vertical abs horizontal asymptotes. 3.Find the end behavior of the function (y,y)
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