A Treatise On the Differential Calculus With Numerous Examples
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But instead of solving the given equation we may proceed thus : by Art. 177, fdu\ dy _ \dx) ^ dx /du\ ' where u stands for ^ (a?, y). But the values of x which make y a maximum or minimum must, by Art. 211, bei found by isolving the equation ^ = 0. Hence ity :0, and this equation, combined with k = 0, will determine the values of x, which may make y a maximum or minimum.
To determine whether such a value of x does make y a Digitized by VjOOQ IC OF AN IMPLICIT FUNCTION. 197 maximum or minmmm, we... must, by Art. 211, examine the value of ^ . B7 Art, 180, since f ^J = 0, we have \dy) Hence we have this rule : To find the maxin^a or minima values of y, which is an implicit function of a: determined by ti = 0, we must find values of x and y which satisfy w = and {j- j = 0. If when these values are substituted in ^-r— . [dxV w the fraction is positive, we have obtained a maximum value of y ; if the firaction be negative, we have a minimum value of y.
Ex. If af-Zaxy^y' = (1), find the maxima or minima values of y.
What to read after A Treatise On the Differential Calculus With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
But instead of solving the given equation we may proceed thus : by Art. 177, fdu\ dy _ \dx) ^ dx /du\ ' where u stands for ^ (a?, y). But the values of x which make y a maximum or minimum must, by Art. 211, bei found by isolving the equation ^ = 0. Hence ity :0, and this equation, combined with k = 0, will determine the values of x, which may make y a maximum or minimum.
To determine whether such a value of x does make y a Digitized by VjOOQ IC OF AN IMPLICIT FUNCTION. 197 maximum or minmmm, we... must, by Art. 211, examine the value of ^ . B7 Art, 180, since f ^J = 0, we have \dy) Hence we have this rule : To find the maxin^a or minima values of y, which is an implicit function of a: determined by ti = 0, we must find values of x and y which satisfy w = and {j- j = 0. If when these values are substituted in ^-r— . [dxV w the fraction is positive, we have obtained a maximum value of y ; if the firaction be negative, we have a minimum value of y.
Ex. If af-Zaxy^y' = (1), find the maxima or minima values of y.
What to read after A Treatise On the Differential Calculus With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
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