= Linear interpolant
{title2=$p(x)=\dfrac{b-x}{b-a}y_a+\dfrac{x-a}{b-a}y_b$}
A <linear interpolant> is the unique <polynomial> of <polynomial degree> at most one taking prescribed values $y_a,y_b$ at distinct <interpolation nodes> $a,b$. It is an <affine function>, including the <constant function> case. For $a\leq x\leq b$, its two displayed <coefficients> are nonnegative and sum to one, so changing each sampled value by at most $\delta$ changes every interpolated value by at most $\delta$. Differentiation instead uses the difference of the two samples divided by $b-a$, causing <noise amplification by differentiation of a linear interpolant>.
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