Derivative

Error function is a parabola. Can find its minimum by taking the derivative and setting it to zero.

• $D(E(c)) = D(\sum_{i=1}^n (y_i-c)^2)$
• $= \sum_{i=1}^n D((y_i-c)^2)$
• $= \sum_{i=1}^n 2 (y_i-c) D((y_i-c))$
• $= 2 \sum_{i=1}^n (c-y_i)$
• $= 2nc - 2 \sum_{i=1}^n y_i$

• D(E(c)) = 0
• $2nc - 2 \sum_{i=1}^n y_i = 0$
• $2nc = 2 \sum_{i=1}^n y_i$
• $c = \sum_{i=1}^n y_i/n$