2.6 Tangent Lines and Their Slopes

By the end of your studying, you should know:
Onscreen applet instructions: Note that the tangent line is the dotted blue line. Use the slider to control the position of the point Q (hence the secant line and its slope m).
ExamplesCan you find a tangent line to f(x) = x at x = 0?A practice ski jump hill follows the shape of a given curve. Come up with a formula for the angle the skier's skis make with the horizontal, and find how far from the top of the jump he is when this angle is the greatest. A potted cactus is thrown upward with a velocity of 40 feet per second. Its height in feet at time t is given by the formula h(t) = 40t – 16t^{2}. Find its velocity 2 seconds after it is released. AppletsSecant and Tangent Lines
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.6 Tangent Lines and Their Slopes (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications

2.5 Continuity  Table of Contents  2.7 The Derivative 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel