First view extrema and points of inflection

If all eigenvalues are different, the following equations are valid in the concentration-time diagrams for extrema 

If at least one of the s parameters differs from zero, neither extrema nor points of inflection are found in concentration-time diagrams. For example, assuming the values p, and p,2 are different from zero, eqs. (2.64) and (2.65) can be solved with respect to t. As soon as the concentrations either reach a minimum or a maximum (index m) one obtains 

If they reach a point of inflection (index w), one obtains 

In consequence, one finds, for any component Ai for which exactly two of the parameters differ from zero as the distance between the extrema and the point of inflection within a concentration-time diagram in general. 

For the special case of two linear independent steps of a reaction (s = 2), the following two equations are valid [16]  

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