Arthur Ernest Jolliffe, 1911 Encyclopædia Britannica, Volume 17… (1911)
“ A critical value usually gives a maximum or minimum in the case of a function of one variable, and often in the case of several independent variables, but all maxima and minima, particularly absolutely greatest and least values, are not necessarily critical values. ”
Arthur Ernest Jolliffe, 1911 Encyclopædia Britannica, Volume 17… (1911)
“ Now, the quantities being all positive, the product cannot be increased without limit and must somewhere attain a maximum, and no other form of the product than that in which they are all equal can be the maximum, so that the product is a maximum when they are all equal. Its minimum value is obviously zero. If the restriction that all the quantities shall be positive is removed, the product can be made equal to any quantity, positive or negative. ”
Arthur Ernest Jolliffe, 1911 Encyclopædia Britannica, Volume 17… (1911)
“ Hence Σ (δu/δx1) δx1 must vanish for all sets of increments δx1, . . . δxn, and since these are independent, we must have δu/δx1 = 0, δu/δx2 = 0, . . . δu/δxn = 0. A value of u given by a set of solutions of these equations is called a “critical value” of u. The value of δu now becomes for u to be a maximum or minimum this must have always the same sign. ”
