= Steepest ascent in response surface methodology
{title2=$d=\widehat b/\|\widehat b\|$}
For a fitted local first-order response $\widehat m(x)=\widehat\beta_0+\widehat b^Tx$, the unit direction maximizing its directional derivative in coded Euclidean distance is $d=\widehat b/\|\widehat b\|$, by the <Cauchy-Schwarz inequality>. Run sequential feasible settings $x_0+hd$, increase $h$ while measured response improves, and refit near promising settings. Physical increments are $h_jhd_j$, so coded and unscaled physical gradients need not give the same experimental path. A near-zero gradient calls for further modeling rather than division by zero.
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