= Three-point asymmetric second-derivative formula
{title2=$f''(2)\approx\frac23f(0)-f(1)+\frac13f(3)$}
Matching the monomials $1,x,x^2$ gives $f''(2)\approx(2/3)f(0)-f(1)+(1/3)f(3)$. With error defined as the true derivative minus this approximation, its <Peano kernel> is $K(\theta)=2\mathbf1_{\{\theta<2\}}+(1-\theta)_+^2-(3-\theta)^2/3$ on $[0,3]$. The derivative evaluation causes a jump at two. Applying the <Peano kernel theorem> gives $\lambda(f)=\tfrac12\int_0^3Kf^{(3)}$.
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