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.

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

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