The discussion revolves around finding critical numbers for the function g(t) = 5^(2/3) + t^(5/3) and its derivative g'(t). Participants are exploring the implications of setting the derivative equal to zero and the proper handling of exponents in the expressions.
The discussion is active, with participants providing guidance on factoring and clarifying notation. There is an acknowledgment of the critical point at T = 0, although no consensus on the next steps has been reached.
There is a noted confusion regarding the use of "T" and "t" in the expressions, which may affect the clarity of the discussion. Additionally, the derivative's behavior at T = 0 is highlighted as a critical point, but the implications of this are still being explored.
I assume you meant g(T)= 6T^(2/3)+ T^(5/3).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