. Differential and integral calculus, an introductory course for colleges and engineering schools. e symbols Ax and Af(x), the first of whichis read increment x or delta x, and the second incrementfunction x or delta function x. Moreover, we shall usuallyomit the subscripts and write x, x + Arc for the two values of theargument. Then the foregoing identity takes the form(i) Af(x)^f(x + Ax)-f(x)* If y denote the functional symbol, the increment of y is Ay. Letx, f(x) be the coordinates of a point P on the graph of f(x). Theabscissa of a second point Q may be denoted by x + Ax, and thenthe ordin
. Differential and integral calculus, an introductory course for colleges and engineering schools. e symbols Ax and Af(x), the first of whichis read increment x or delta x, and the second incrementfunction x or delta function x. Moreover, we shall usuallyomit the subscripts and write x, x + Arc for the two values of theargument. Then the foregoing identity takes the form(i) Af(x)^f(x + Ax)-f(x)* If y denote the functional symbol, the increment of y is Ay. Letx, f(x) be the coordinates of a point P on the graph of f(x). Theabscissa of a second point Q may be denoted by x + Ax, and thenthe ordinate of Q will be denoted by f(x + Ax) or f(x) + Af(x).The line segments representing Ax, Af(x), etc., are shown in theaccompanying figures. In the second figure Af(x) is negative. * A result of this omission of the subscript is that we use x and f(x) sometimesto denote argument and function in general and sometimes to denote fixedvalues of them. This will occasion no difficulty to the careful student, and theuse of the subscript would cumber the formulae unnecessarily. 32 22 THE DERIVATIVEY 33. f(x)+Wx) X O
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