cost

[Var1995]

 AVC is at its maximum value for the TC fn 40+82q-6q^2+0.2q^3 at q= 15, but when i took the second derivative of AVC, it's coming out to be >0 but it should be <0. can someone point out my mistake, please?

[Dr. Strange]

AVC is minimum at Q=15 and not maximum.

Expression fr VC=82Q -6Q^2 +0.2 Q^3

Expression fr AVC=82-6Q+0.2Q^2

Expression fr AVC reduces to 1/5*(Q-15)^2 + 37

Surely at Q=15 it attains minima

[Var1995]

i m not getting the 3rd expression

[Dr. Strange]

I just rearranged the previous expression of AVC by making whole square .
You don't need to do it.
Your analysis by calculus is right.
Second derivative is positive so its a minima.

[Var1995]

Okay