Mathematics for engineering students, Analytical geometry and calculus (1907)
Keller, S. S. (Samuel Smith), 1867-1923, Knox, W. F., [from old catalog] joint author · New York : D. Van Nostrand company · leaf 285
is a maximum point for the valuex = OD. A glance at the figure will show that starting,say with the tangent MN at A, the slope of this tangent asthe point of tangency moves from A to T will be constantlypositive (the inclination being an acute angle, as AMO) butconstantly decreasing; at T the slope… … Fig. 23. in general. Therefore, as indicated, the derivative of thefunction which is always equal to these slopes, will passfrom positive to negative through zero. But a functionmay pass through zero or infinity without changing itssign, so even when the derivative is zero there may not be amaximum…
Geometry, Analytic · Calculus
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