2.7 The Derivative
By the end of your studying, you should know:
On-screen applet instructions: Use the slider to control the value of h. Note that the number of difference quotients computed and plotted increases as h->0. The button under the slider shows and hides the derivative curve. Whenever you like, you can compare a computed set of difference quotients with the derivative. What is the geometrical significance of the limit of the difference quotient as h -> 0?
ExamplesLet f(x) = x2 and g(x) = x. Find (f + g)' (4). Does this equal f '(4) + g'(4)?
VideosSee short videos of worked problems for this section.
ExercisesSee Exercises for 2.7 The Derivative (PDF).
Work online to solve the exercises for this section, or for any other section of the textbook.
Resources on the WebInformation on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Average reaction rates and instantaneous reaction rates in chemistry can be quite different.
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel