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Introduction to Derivatives In this chapter we will be understand what a derivative is, how to tell if it exists or not, and how to find it if it
 

Summary: Chapter 3
Introduction to Derivatives
In this chapter we will be understand what a derivative is, how to tell if it exists or not, and how to find it if it
does. The ideas of limits and continuity of a function are pillars on which we build the derivative so we begin
with those concepts.
Calculus required continuity, and continuity was supposed to require the
infinitely little; but nobody could discover what the infinitely little might
be.
­ Bertrand Russell
Yet in another way, calculus is fundamentally naive, almost childish in
its optimism. Experience teaches us that change can be sudden, dis-
continuous, and wrenching. Calculus draws its power by refusing to see
that. It insists on a world without accidents, where one thing leads log-
ically to another. Give me the initial conditions and the law of motion,
and with calculus I can predict the future ­ or better yet, reconstruct the
past. I wish I could do that now.
­Steven Strogatz
Calculus has its limits.
­ Anon.
3.1 Limits and Continuity

  

Source: Ashlock, Dan - Department of Mathematics and Statistics, University of Guelph

 

Collections: Mathematics