- #1
Read carefully.Karol said:Homework Statement
View attachment 230882
Homework Equations
Minimum/Maximum occurs when the first derivative=0
The Attempt at a Solution
$$R'=2D\left( \frac{C}{2}-\frac{D}{3} \right)-\frac{1}{3}D^2$$
$$R'=0~\rightarrow~D=C$$
Read the problem again. It's R'(D) which you need to find the maximum for, not finding the maximum for R(D) .Karol said:$$R'=2D\left( \frac{C}{2}-\frac{D}{3} \right)-\frac{1}{3}D^2,~~R''=C-2D,~~R''=0:~D=\frac{C}{2}$$
But the greatest change in R for a small change in D is where R has a maximum, hence where R'=0, not where R''=0
Karol said:Yes, that's correct, i need the maximum for R', but why?
At the point where R has a maximum, i think, a small change in D makes a big change in R
Karol said:Yes, that's correct, i need the maximum for R', but why?
At the point where R has a maximum, i think, a small change in D makes a big change in R
Min max refers to the minimum and maximum values of a given variable. In the context of medicine, it is used to determine the optimal amount of a medication that will provide the most benefit with the least amount of side effects.
The optimal quantity of medicine is determined by finding the minimum effective dose that achieves the desired therapeutic effect, while also identifying the maximum tolerable dose that does not cause harmful side effects. The ideal quantity of medicine lies somewhere between these two values.
The factors that are considered include the patient's age, weight, medical history, current health condition, and severity of the illness. The type and strength of the medication, as well as any potential drug interactions, are also taken into account.
Yes, the optimal quantity of medicine can change over time. Factors such as changes in the patient's health status, the development of new medications, and adjustments in the recommended dosages can all impact the optimal quantity of medicine.
Finding the optimal quantity of medicine can benefit patients by minimizing the risk of harmful side effects while still providing the desired therapeutic effect. It also helps to optimize the use of medication and reduce unnecessary costs associated with over or under-medication.