Marginal Cost

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1.Differentiate the following:
(a)y = 10 x3 - 10 x2 + 4x + 2(e)y = [pic]
(b)y = [pic](f)y = ( 4 + x ) ( x - 1 )
(c)y = [pic](g)2y = 3 x2 + 10
(d)y =[pic](h)x y = 2 x2 - 5 x + 4

2.Find the integral of the following:
(a) [pic](e)[pic]
(b) [pic](f) [pic]
(c) [pic](g) [pic]
(d) [pic]

3.Find the x value of the turning points on the graph of y = [pic] and determine whether it is a maximum or a minimun point.

4.Find the coordinates of the two turning points of the function y = x3 - 8 x2 + 5 x + 3

5.For a particular function, dy/dx = 4x - 3. If it is known that when x = 1, y = 5, find y in terms of x.

6.A manufacturing process costs RM 6500 to set up for one year’s use. If items cost RM 85 each to produce and other costs amount to 3.5 x2, where x is the production in hundreds, find the level of production that will minimise the cost per item over the year. What will the total cost amount to at this level of production?

7.The marketing department of Spager Ltd estimated that if the selling price of product is set at $15 per unit then the sales will be 50 units per week, while, if the selling price is set at $20 per unit, the sales will be 30 units per week. Assume that the graph of this function is linear. The production department estimates that the variable cost will be $5 per unit and that the fixed cost will be $50 per week, and special cost are estimated as $0.125x2, where x is the quantity of output. All production is sold. (a) Show that the relationship between price (Pr) and quantity sold (x) , are given by the equation Pr = 27.5 - 0.25x. (b) Find the revenue function, R.

(c) Find the total cost function (C).
(d) Advise the company on production and pricing policy if it wishes to maximize profits, and find the maximum profit.

8.A firm receives £135 for each unit sold. The costs consist of a fixed cost per month of £2500 and...
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