Hello, I wanted to know if someone could correct this exercise if possible because I did not understand much in it, even for the sign table. Analyzes have shown that microalgae are naturally present in seawater, with a normal concentration between 0 and 100 milligrams per liter (mg/L).

These microalgae tend to multiply when the salinity of the sea water decreases, the evolution of the concentration of microalgae in the bathing water of a coastal beach during the 10 days which followed a very strong courage modeled by the function F defines the interval 0 or 10 by f(x) = x^3-21x^2+120x+50.Health authorities predict that they become dangerous to health when their concentration exceeds 200 mg/L. It is then necessary to take measures such as the prohibition of bathing.Where x is the translated time after the storm expressed in daysThe derivative f'(x) = (3x-12)(x-10)

1) Study the sign of the derivative f'(x) on the interval [0;10].

2) Indicate the period during which swimming is prohibited

3) Determine the maximum microalgae concentration during the 10 days following the storm