103Lab04Soln.pdf - MA103 Lab Report 4 Derivatives Continued...

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MA103 Lab Report 4 - Derivatives Continued Name: Student Number: Fall 2020 1. [5 marks ] Suppose that Major League Baseball (MLB) has determined that the relationship between the demand q for World Series tickets and each ticket’s price p is given by 0 . 005 p - 15 ln p = 2 - 10 ln q. [Note: This is called the demand equation .] (a) Use implicit differentiation to find dq dp .
(b) It can be shown that MLB will have their greatest revenue (i.e. generate the most money from ticket sales) when the elasticity of demand E = - p q dq dp = 1 . Find the price p that each World Series ticket should be sold for in order to maximize revenue.
2. [6 marks ] Suppose y = ( e x tan x ) tan - 1 x . (a) Using properties of logarithms, show that ln y = x tan - 1 x + tan - 1 x ln(tan x ).

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