L1 Limits, Secants, and Tangents - Part 3
Completion requirements
Unit 2A
Derivatives Part 1
Lesson 1: Limits, Secants, and Tangents
Finding the slope of a curve requires some careful thought. Of particular note is the fact the slope of a curve will not be the same everywhere on the curve. In some intervals, the slope will be clearly negative (down to the right). In other intervals,
the slope will be clearly positive (up to the right). And, at some points, the slope will be zero (horizontal).
Click the interactive button to open the applet Secant Line Slope Calculator. This applet approximates the slope of a curve at point «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«/mstyle»«/math» by generating secant lines and calculating their slopes.
To use the applet, move the second point along the curve. The black line through point A and the second point is called a secant line. Secant lines pass through at least two points on a curve. Note the slope of the secant line varies as the second point is moved. To calculate the slope of each secant line, the slope formula «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»m«/mi»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»y«/mi»«mn»2«/mn»«/msub»«mo»§#8722;«/mo»«msub»«mi»y«/mi»«mn»1«/mn»«/msub»«/mrow»«mrow»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»§#8722;«/mo»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» is used.
Interactive
Click the interactive button to open the applet Secant Line Slope Calculator. This applet approximates the slope of a curve at point «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»A«/mi»«/mstyle»«/math» by generating secant lines and calculating their slopes.
To use the applet, move the second point along the curve. The black line through point A and the second point is called a secant line. Secant lines pass through at least two points on a curve. Note the slope of the secant line varies as the second point is moved. To calculate the slope of each secant line, the slope formula «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»m«/mi»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»y«/mi»«mn»2«/mn»«/msub»«mo»§#8722;«/mo»«msub»«mi»y«/mi»«mn»1«/mn»«/msub»«/mrow»«mrow»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»§#8722;«/mo»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» is used.