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MATHEMATICS - CASE STUDY

    Introduction



Plant Cells

 

Man-made Auxin, a growth chamical, can accelerate the growth speed of plant cells. The cell elongation speed can be modeled with a mathematic expression. To better understand the relationship between the elongation speed and time, the mathematic expression can be plotted.

What is known:

  • The mathematics relationship between the promoted elongation speed and the time is
          f(t) = -t3 + 5t2 - 3t + 5
  • The life cycle of Auxin is 7 weeks
  • The unit for elongation speed and time is μm/week and week, respectively.
     
    Questions

 

 

Sketch the curve of the function and show all key features.

     
    Approach

 

 
  • Find the domain and intercepts of the function.
  • Analysis the symmetric, asymptote, monotonocity, local extreme value, concavity and inflection points of the function.