Another critical numbers problem

  • Thread starter afcwestwarrior
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I assume you mean g'(T)= 10/3T^(-1/3)+ 5/3t^(2/3). In summary, to solve for g'(T)= 0, you can factor out a t^(-1/3) and multiply the entire equation by t^(1/3).
  • #1
afcwestwarrior
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g(T)=5^2/3+ t^5/3

g't= 10/3T^-1/3+ 5/3t^2/3

ok do i factor this one out, this one looks confusing
 
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  • #2
Are you trying to solve g'(t)=0? Then sure, factor out a t^(-1/3).
 
  • #3
remember that when it says ^-1/3
its not saying (5t^-1)/3
 
  • #4
That's why I put parentheses around the (-1/3). You should too.
 
  • #5
afcwestwarrior said:
g(T)=5^2/3+ t^5/3

g't= 10/3T^-1/3+ 5/3t^2/3

ok do i factor this one out, this one looks confusing
I assume you meant g(T)= 6T^(2/3)+ T^(5/3).

After you got g'(T)= (10/3)T^(-1/3)+ (5/3)T^(2/3)= 0 you can multiply the entire equation by T^(1/3). (Obviously, the derivative does not exist at T= 0 so that is also a critical point.)

It's a lot easier to read with parentheses! Also, please do not use "T" and "t" to mean the same thing.
 

1. What is a critical number?

A critical number is a value in a function where the derivative is either equal to zero or does not exist. It is important because it helps us determine the maximum and minimum values of a function.

2. How do you find critical numbers?

To find critical numbers, you first need to find the derivative of the function. Then, set the derivative equal to zero and solve for the variable. Any values that satisfy this equation are considered critical numbers.

3. Why are critical numbers important in mathematics?

Critical numbers are important because they help us determine the behavior of a function. They can help us find the maximum and minimum values, as well as identify points of inflection.

4. Can a function have more than one critical number?

Yes, a function can have multiple critical numbers. This can happen when the derivative is equal to zero at multiple points or when it does not exist at multiple points.

5. How are critical numbers used in real-life applications?

Critical numbers are used in real-life applications such as optimization problems in economics, engineering, and physics. They can also be used to analyze the behavior of a system in order to make predictions and improve performance.

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