Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 155
phof a function runs up toward the right handwhen the function is increasing and runsdown toward the right hand when the func-tion is decreasing. Thus x~— x — 6 (fig. 119)is decreasing when x < \ and increasing whenx>\. The sign of the derivative enables us todetermine whether a function is… … SIGN OF THE DEKIYATIVE 139 To prove this, consider y =f(x), and let us suppose that — is positive. Then, since -~ is the limit of —, it follows that —-dx dx Ax Ax is positive for sufficiently small values of Ax; that is, if Axis assumed positive, Ay is also positive, and the function is increasing.…
Geometry, Analytic · Calculus
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