Minimum and maximum of an equation

[Gear300]

The problem here is relatively simple...I just need to confirm something:

A + B - C = D, in which B is a function of A and C is constant.
dD/dA = 1 + dB/dA for the derivative
To find a min/max of D for certain angles of A,
dD/dA = 0 = 1 + dB/dA
dB/dA = -1
dB = -dA
B = -A, which would imply that D is a min/max where B = -A and dB/dA = -1
D_min/max = A - A - C
D_min/max = -C, and thus D is a min/max where it is equivalent to -C.

Was my mathematics wrong anywhere in there?

 

[Mark44]

The problem here is relatively simple...I just need to confirm something:

A + B - C = D, in which B is a function of A and C is constant.
dD/dA = 1 + dB/dA for the derivative
To find a min/max of D for certain angles of A,
dD/dA = 0 = 1 + dB/dA
dB/dA = -1
dB = -dA
B = -A, which would imply that D is a min/max where B = -A and dB/dA = -1
D_min/max = A - A - C
D_min/max = -C, and thus D is a min/max where it is equivalent to -C.

Was my mathematics wrong anywhere in there?

If dB/dA = -1, then B = -A + a constant. IOW, the graph of B is a straight line with slope -1. Also, dD/dA = -A + a different constant.

 

[Gear300]

I see...thank you