A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xviii
... MAXIMA AND MINIMA . 144. Definition of maximum and minimum 235 SECTION 1. - Maxima and minima of explicit functions of one variable . 145. Method of determining such singular values of ƒ ( x ) . 146. Easy detection of the singular ...
... MAXIMA AND MINIMA . 144. Definition of maximum and minimum 235 SECTION 1. - Maxima and minima of explicit functions of one variable . 145. Method of determining such singular values of ƒ ( x ) . 146. Easy detection of the singular ...
Page xix
Bartholomew Price. 159. Application of the method to total minima 160. The sufficiency of the process 161. Examples of the process 162. A consideration of a case wherein the requisite conditions are not fulfilled SECTION 4. - Maxima and ...
Bartholomew Price. 159. Application of the method to total minima 160. The sufficiency of the process 161. Examples of the process 162. A consideration of a case wherein the requisite conditions are not fulfilled SECTION 4. - Maxima and ...
Page 234
... .3 + 3ƒ " ( aoo ) ( α10x + α01y ) ( α20x2 + 2α11 xy + α02 y2 ) + ƒ ' ( aoo ) ( α30 x3 +3 а21 x2y +3 α12xy2 + α03 Y3 ) ] + .... . ( 60 ) CHAPTER VII . ON THE DETERMINATION OF MAXIMA AND MINIMA 234 [ 143 . FUNCTIONS OF MANY VARIABLES .
... .3 + 3ƒ " ( aoo ) ( α10x + α01y ) ( α20x2 + 2α11 xy + α02 y2 ) + ƒ ' ( aoo ) ( α30 x3 +3 а21 x2y +3 α12xy2 + α03 Y3 ) ] + .... . ( 60 ) CHAPTER VII . ON THE DETERMINATION OF MAXIMA AND MINIMA 234 [ 143 . FUNCTIONS OF MANY VARIABLES .
Page 235
Bartholomew Price. CHAPTER VII . ON THE DETERMINATION OF MAXIMA AND MINIMA VALUES OF FUNCTIONS . 144. ] LET us consider a function of a single variable x ... MAXIMA AND MINIMA . CHAPTER VII MAXIMA AND MINIMA Definition of maximum and minimum.
Bartholomew Price. CHAPTER VII . ON THE DETERMINATION OF MAXIMA AND MINIMA VALUES OF FUNCTIONS . 144. ] LET us consider a function of a single variable x ... MAXIMA AND MINIMA . CHAPTER VII MAXIMA AND MINIMA Definition of maximum and minimum.
Page 236
... maximum value ; and if r ' ( x ) changes its sign from to + , we have a minimum value ; and as changes of sign can take place only when the quantity passes through O or∞ , we have the following rule to determine Maxima and Minima ...
... maximum value ; and if r ' ( x ) changes its sign from to + , we have a minimum value ; and as changes of sign can take place only when the quantity passes through O or∞ , we have the following rule to determine Maxima and Minima ...
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according algebraical angles applicable assume axis becomes Calculus called changes sign Chapter circle coefficients consider constant continuous corresponding curve derived derived-functions determine differential dimensions direction divided drawn dx dy dy dx elimination equal equation examples expression factors finite function geometrical given gives greater Hence homogeneous function increases independent infinite infinitesimal infinity involved less limit maxima maximum means method minima minimum value negative observed origin partial particular pass plane positive powers preceding properties quantity relation replaced represent respectively result roots sides similar Similarly singular value straight line substituted successive suppose symbols tangent Theorem tion true values vanish variables variation vary whence zero