Question

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Calculus (4 marks) A firm estimates that the total revenue, SR(q), received from the sale of q goods is given by 5. R(x) = ln(1 + 1000 ) Calculate the marginal revenue when q = 10. Explain what this result means. 6, (3 marks) Consider the function f(x) = x3 + 2. (a) Sketch a graph of y-f(x) on I-1,2 (b) Estimate the area bounded by y-f(x), the x-axis and the linesx-1, x approximation with 3 equal subdivisions. 2 by using an upper sum e) Discuss how your estimate could be improved. 7. (8 marks) An amusement park ride is constructed such that its height h in metres above the ground can be expressed in terms of the horizontal distance x from the starting point. h(x) is given by ㄫㄨ h(x) = 50 + 45 sin-, 50 0 105 x (a) Determine h(x) (b) Calculate h'(40) and interpret your result. (c) Using calculus, find the maximum and minimum height of the ride. (d) (8 marks) Given that h (x)=-45 50 2 sinnt find (using calculus) the distance from the starting point at which the rides rate of change is the greatest.

Answer 1

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