Theory of Maxima And Minima
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It follows that G (0, 0) is not an extreme of G (x, a;), and as both limits begin with powers of x not exceeding the fourth, the Scheeffer theorem is applicable, which shows that/(0, 0) is not an extreme of f(x, y).
(/?) ac b 2 > 0. It follows since a > that c must also be positive. The two limits just derived are both positive. Continuing we must next deter mine the other two limits. When y is constant and | x \ = | y \, we have by solving the equation = = 4 x (by + ex 2 ) CX : the two values ...x = and x = \! y-.
\ c 60 THEOKY OF MAXIMA AND MINIMA If b ^ the latter value may be neglected ( 38), since the exponent of y lies between and 1. If & = 7 this value coincides with the first. We observe that each of the functions G (0, y) = ay* and G ( y, y} = af + 2 % 3 + cy* is positive. It follows from Stolz s theorem that G (0, 0) is a proper mini mum of G (x, y} ; and since the power of x or y on the right-hand side of any of the four limits is not greater than 4, the Scheeffer theorem shows that/(0, 0) is a proper minimum of f(x, y).
What to read after Theory of Maxima And Minima?
You can find similar books in the "Read Also" column, or choose other free books by Harris Hancock to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
It follows that G (0, 0) is not an extreme of G (x, a;), and as both limits begin with powers of x not exceeding the fourth, the Scheeffer theorem is applicable, which shows that/(0, 0) is not an extreme of f(x, y).
(/?) ac b 2 > 0. It follows since a > that c must also be positive. The two limits just derived are both positive. Continuing we must next deter mine the other two limits. When y is constant and | x \ = | y \, we have by solving the equation = = 4 x (by + ex 2 ) CX : the two values ...x = and x = \! y-.
\ c 60 THEOKY OF MAXIMA AND MINIMA If b ^ the latter value may be neglected ( 38), since the exponent of y lies between and 1. If & = 7 this value coincides with the first. We observe that each of the functions G (0, y) = ay* and G ( y, y} = af + 2 % 3 + cy* is positive. It follows from Stolz s theorem that G (0, 0) is a proper mini mum of G (x, y} ; and since the power of x or y on the right-hand side of any of the four limits is not greater than 4, the Scheeffer theorem shows that/(0, 0) is a proper minimum of f(x, y).
What to read after Theory of Maxima And Minima?
You can find similar books in the "Read Also" column, or choose other free books by Harris Hancock to read onlineMoreLess
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