Slopes, Derivatives, and Tangents（斜坡、衍生品和切线）.pdfVIP

Slopes, Derivatives, and Tangents Matt Riley, Kyle Mitchell, Jacob Shaw, Patrick Lane S Introduction Definition of a tangent line: The tangent line at a point on a curve is a straight line that “just touches” the curve at that point S  The slope of a tangent line at a point on a curve is known as the derivative at that point S  Tangent lines and derivatives are some of the main focuses of the study of Calculus S  The problem of finding the tangent to a curve has been studied by numerous mathematicians since the time of Archimedes. Archimedes A Brief History S  The first definition of a tangent was a right line which touches a curve, but which when produced, does not cut it. This old definition prevents inflection points from having any tangent. It has since been dismissed. -  Leibniz, a German philosopher Pierre de Format and mathematician, defined the tangent line as the line through a Gottfried Wilhelm Leibniz pair of infinitely close points on the curve. -  - Pierre de Format, Rene’ Descartes, Christian Huygens, and Isaac Barrow are mathematicians given credit for finding partial solutions. -  - Isaac Newton is credited for Rene’ Descartes finding the general solution to the tangent line problem. Isaac Newton Visual Web Implicit Vector Derivatives Differentiatio Calculations n Trigonometric Equations Calculus Pre-Calc