12 Optimisation

12 Optimisation - 12.OPTIMISATION 1. For a > 0...

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Unformatted text preview: 12.OPTIMISATION 1. For a > 0 the line x a y a a- = + ) 1 ( 2 forms a triangle in the first quadrant with the x- and y-axes. (a) [2 marks] Find the x- and y- intercepts of the line in terms of a . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b) [2 marks] Find the area of the triangle as a function of a . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [6 marks] Find analytically the value of a which maximises the area. Fully justify your answer. What is the value of the maximum area? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 70 12. Optimisation 2. Suppose that ) 1 2 )( 4 ( ) ( 2-- = x x x f and 4 ) ( 2- = x x g The line p x = , where 0 < p < 2, intersects the graph of f at point A and the graph of g at point B. A triangle has vertices A, B and the origin O. (a) [2 marks] Draw a sketch showing the graphs of the functions f and g , the line p x = and points A, B and O. (b) [5 marks] Write the area of triangle OAB as a function of p . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________...
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This note was uploaded on 09/01/2010 for the course MATH MAT1300 taught by Professor Mcdonald during the Spring '10 term at Acadia.

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12 Optimisation - 12.OPTIMISATION 1. For a > 0...

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