Can somebody help me with Math?
1.) A pool is treated with a chemical to reduce the amount of algae in the pool. The algae concentration t days after the treatment can be approximated by the function A(t)=42(t)^2 – 252t + 600, where A(t) is measured in micrograms of algae per liter of pool water. How many days after the treatment will the pool have the lowest concentration of algae?
2.) A manufacturer of microwave ovens believes that the revenue R, in dollars, the company receives is related to the price P, in dollars, of an oven by the function R(P) = 110P – 0.2(P)^2. What price will give the maximum revenue?
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Thanks
if you want to know the maximum or the lowest value of a function f(x), you just have to solve f'(x)=0
A(t)=42*t^2-252*t+600
A'(t)=2*42*t-252
84t-252=0
84t=252
t=252/84=3 days
R(p)=110p-0.2*p^2
R'(p)=110-2*0.2*p
110-0.4*p=0
0.4p=110
p=110/0.4=275 $
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