Differentiate equation TC with respect to T

Questions
1

TC == 1/T {ChD1(([Lambda](c(s-1)-td)(T-td)^2)/2+
(a(T+c(1-s))(T-td)^b+1)/(b+1)-(2a(T-td)^b+2)/((b+1)(b+2))+
T^2/2-((T^3)[Lambda])/3 +
T^2[Lambda]td-(3T[Lambda]td^2)/2+([Lambda]td^3)/6)+K}
/.{D1 → 4000, c → 10, Ch → 2, s → 0.1, K → 200,a → 0.2, b → 1.5,td → 20/365,
[Lambda] → 0.2}
D[TC, T]==0

Please evaluate.

2

ClearAll["`"]
TC = Rationalize[
1/T {ChD1 (([Lambda](c(s - 1) - td)(T - td)^2)/
2 + (a(T + c*(1 - s))(T - td)^b + 1)/(b +
1) - (2a*(T - td)^b + 2)/((b + 1)(b + 2)) +
T^2/2 - ((T^3) [Lambda])/3 +
T^2[Lambda]td - (3 T[Lambda]td^2)/
2 + ([Lambda]td^3)/6) + k} /. {D1 → 4000, c → 10,
Ch → 2, s → 0.1, k → 200, a → 0.2, b → 1.5,
td → 20/365, [Lambda] → 0.2}, 0][[1]] // FullSimplify
((200 + 8000 (2334134/5835255 - 4/35 (2 + 2/5 (-(4/73) + T)^(3/2)) - (
11203068469727 (-(4/73) + T)^2)/12372526449169 - (24 T)/26645 + (
373 T^2)/730 - T^3/15 + 2/25 (-(4/73) + T)^(3/2) (9 + T)))/T)

 func = D[TC, T] // FullSimplify
 (*-(2850630093888538400/903194430789337) + 
  960 Sqrt[-(4/73) + T] + (-(156639186421396108130600/
    101075585555203914333) + 151040/511 Sqrt[-(4/73) + T])/T^2 + (
  18880 Sqrt[-(4/73) + T])/(7 T) - (3200 T)/3*)

  Solve[func == 0, T] // N
  (*{{T -> -3.03984 - 0.158213 I}, {T -> -3.03984 + 0.158213 I}, {T -> 
     0.582782 - 0.712647 I}, {T -> 0.582782 + 0.712647 I}}*)