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MATHEMATICS - CASE STUDY

    Introduction


Experiment Equipments

 

A group of college students in a chemistry lab are asked to find the maximum mass density of an unknown liquid between 0oC and 40oC. After they performed the experiment multiple times at different temperature, they determined the volume is a function of temperature. They summerized the formula to calculate the volume v of 1 kg at temperature t. It is

    v = 999.87 - 0.06426T + 0.0085T2 - 0.00006T3

    Questions

 

 

At what temperature is the density a maximum?

     
    Approach


 
  • The critical point of the mass density and the volume are the same.
  • Maximum and minimum values may be located at critical points or boundary.