Determining the path of steepest ascent

The arrow in Fig. 6.3 indicates the path of steepest ascent starting at the center point. The direction of this path can be determined algebraically from the model coefficients. For maximum inclination, we must move in steps taken with a 62/ 1 ratio along the X2 and Xi axes. 

From Eq. (6.3) we have 62/ 1 = 4.25/(—5.25) =—0.81, which means that for each unit distance receded on the Xi axis we must advance 0.81 units along X2. The coordinates of several points along the path of steepest ascent are presented in Table 6.3, in both coded values and in the concentration and stirring speed units actually used in the laboratory. 

For the general case of a response surface determined by p factors, the steps along the path of steepest ascent are proportional to the magnitudes 

Points on the steepest ascent path for the models of Figs. 6.2 and 6.3 

Then calculate the displacements of the other factors 7 1, in coded units, by means of 

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