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" ... is, the slope of the tangent to the curve) at that point (positive if the tangent points upward, and negative if it points downward, moving to the right). "
The A to Z of Mathematics: A Basic Guide - Page 3
by Thomas H. Sidebotham - 2003 - 488 pages
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Practical Mathematics

John Perry - Mathematics - 1899 - 138 pages
...point of maximum nor minimum. It must be evident to a student that the slope of a curve at a point is the slope of the tangent to the curve at that point. Suppose we want to know the slope at the point P, Fig. 25. Imagine Fig. 26 to be a great magnification...
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An Introduction to the Lie Theory of One-parameter Groups: With Applications ...

Abraham Cohen - Continous groups - 1911 - 268 pages
...it transforms (x,y, y') into (xi,yi,y\}, where, if-(.*,/) is some point on some curve F(x,y) = o,y' is the slope of the tangent to the curve at that point and y\ is the slope of curve F\(xi,y\) = o (into which the other is transformed by the point transformation)...
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Mechanical Engineers' Handbook

Lionel Simeon Marks - Mechanical engineering - 1916 - 1922 pages
...the usual way (Fig. 1), the value of the derivative at any point shows the slope of the curve (that is, the slope of the tangent to the curve) at that point (positive if the tangent points upward, and negative if it pointe downward, moving to the right). The...
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Standard Handbook for Mechanical Engineers

Mechanical engineering - 1916 - 1826 pages
...the usual way (Fig. 1), the value of the derivative at any point shows the slope of the curve (that is, the slope of the tangent to the curve) at that point (positive if the tangent points upward, and negative if it points downward, moving to the right). The...
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1. Mathematical Tables

Edward Vermilye Huntington, Louis Albert Fischer - Engineering - 1916 - 196 pages
...the usual way (Fig. 1), the value of the derivative at any point shows the slope of the curve (that is, the slope of the tangent to the curve) at that point (positive if the tangent points upward, and negative if it points downward, moving to the right). The...
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Handbook of Mathematics for Engineers

Edward Vermilye Huntington - Engineering - 1918 - 226 pages
...the usual way (Fig. 1), the value of the derivative at any point shows the slope of the curve (that is, the slope of the tangent to the curve) at that point (positive if the tangent points upward, and negative if it points downward, moving to the right). The...
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Analytic Geometry: With Introductory Chapter on the Calculus

Claude Irwin Palmer, William Charles Krathwohl - Geometry, Analytic - 1921 - 374 pages
...derivative depends upon the position of Pi on the curve. Definition. — The slope of a curve at any point is the slope of the tangent to the curve at that point. fllJ The notation for the derivative is -j-» read "the derivative dx of у with respect to x." Then...
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Practical Calculus for Home Study

Claude Irwin Palmer - Calculus - 1924 - 476 pages
...the curve. What has been said leads to the following definition: The slope of a curve at any point is the slope of the tangent to the curve at that point. That is, the direction of the curve at any point is the same as the direction of the line tangent to...
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The Practice of Economics: Economic Systems and Decision Making in Western ...

Alex N. McLeod - Business & Economics - 1993 - 386 pages
...synthetic geometry by the equation e=ylmx, where e means elasticity (in this case, elasticity of demand), m is the slope of the tangent to the curve at that point, ' is the abscissa (the distance along the east-west axis), and y is the ordinate (distance along the...
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Lacroix and the Calculus

Joćo Caramalho Domingues - Mathematics - 2008 - 468 pages
...differential equations. A firstorder differential equation gives for each point the value of ^, that is, the slope of the tangent to the curve at that point; starting at a point M, one draws the straight line TMM', such that the tangent of the angle M'MQ (where...
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