Taylor is used to expand in zeta, because zeta is an extreme point, so f' (zeta) = 0.

rule

f(0)=f(ζ)+f'(ζ)(0-ζ)+f''(ζ)/2*ζ^2=- 1+f''(ζ)/2*ζ^2；

f( 1)=f(ζ)+f'(ζ)( 1-ζ)+f''(ζ)/2*( 1-ζ)^2=- 1+f''(ζ)/2*( 1-ζ)^2

Two formulas, one can get zeta when [0, 1/2], the other can get zeta when [1/2, 1], and the other can get zeta when [f'' (zeta) ≥