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 New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | MEDIUM | LARGE Below is the OCR-scanned text from this page: 14 ELEMENTARY ANALYTLCAL METHODS Maxima and Minima 3.4.2 The function y=f(x) has a maximum at x=xo if f'(xo)=O and j"(xo)O. Points zo for which f'(xo) = O are called stationary points. 3.4.3 (2) Functions of Two Variables for those values of (xo, yo) for which (1) Functions of One Variable The functionf(x, y) has a maximum or minimum (a) f(x, y) has a maximum if -<0 w and -0 and ->0 at (xo, yo). 3.5. Absolute and Relative Errors (1) If xo is an approximation to the true value (a) the absolute error of xo is Ax=xo-x, of x, then 3.5.1 x-xo is the correction to x. Ax Ax (b) the relative error of xo is 6x=- =- x xo 3.5.2 3.5.3 (c) the percentage error is 100 times the relative error. 3.5.4 (2) The absolute error of the sum or difference of several numbers is. at most equal to the sum of the absolute errors of the individual numbers. 3.5.5 (3) If f(zl, x2, . . ., 2,) is a function of xl, x2, . . ., xn and the absolute error in xt (i=l, 2, . . . n) is Axz, then the absolute error in f is 3.5.6 (4) The relative error of the product or quotient of several factors is at most equal to the sum of t,he relative errors of the individual factors. 3.5.7 (5) If y=f(x), the relative error 6y=- - f'(') Ax Y f(x) Approximate Values If lel<