Find Maximum of C(T) - Help Needed

  • Thread starter almohandes
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In summary, the purpose of finding the maximum of C(T) is to determine the optimal value of T that will yield the highest possible value for the function C. This can be found using mathematical methods such as differentiation or optimization algorithms. The value of the maximum can be affected by initial conditions, constraints, and the form of the function. It may also change over time if the function is dependent on a variable that changes. However, there are limitations to finding the maximum, as it may not exist or be difficult to determine accurately depending on the form of the function and the methods used.
  • #1
almohandes
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can someone please help me with this, I've been having trouble with it.

C(T)= 2t/(t+3)^2

find the maximum?

thanks
 
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  • #2
Do you know how to find the derivative of the function? If so then check when the slope is equal to 0.
To find the derivative use the (f'(x)g(x) - f(x)g'(x))/(g(x)^2)
 
  • #3
If you've "been having trouble with it", then you must have tried something! What have you tried? Exactly where are you having trouble?
 

1. What is the purpose of finding the maximum of C(T)?

The purpose of finding the maximum of C(T) is to determine the optimal value of T that will yield the highest possible value for the function C. This can be useful in various applications, such as in optimization problems or in determining the maximum efficiency of a system.

2. How is the maximum of C(T) typically found?

The maximum of C(T) is usually found by using mathematical methods, such as differentiation or optimization algorithms. These methods involve taking the derivative of C(T) and setting it equal to 0, then solving for the value of T that maximizes the function.

3. What factors can affect the value of the maximum of C(T)?

The value of the maximum of C(T) can be affected by various factors, such as the initial conditions or constraints of the problem, the form of the function C(T), and the mathematical method used to find the maximum.

4. Can the maximum of C(T) change over time?

The maximum of C(T) can change over time if the function C(T) is dependent on a variable that changes with time. In this case, the maximum may shift as the value of the variable changes.

5. Are there any limitations to finding the maximum of C(T)?

Yes, there are limitations to finding the maximum of C(T) as it is dependent on the form of the function and the accuracy of the mathematical methods used. In some cases, the maximum may not exist or may be difficult to determine accurately.

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