A lady who runs a warehouse has to deal with two large sound speakers that blare out a lot of noise, so she wants to place her desk optimally to minimize total sound. The speakers are 80 metres apart, but one has 3 times the volume of the other. She needs to place her desk in the right place for minimum sound. Because sound quality is inversely proportional to the square of the distance, the function that she needs to w optimize is S(x) = -+ (80 - x ) 2 where x is her distance from the smaller speaker. Use Calculus to determine the value of x that minimizes S. Round x to 2 decimal places and prove that this value produces a minimum using FDT. [7 marks]