MATH 150 - CALCULUS WITH ANALYTIC GEOMETRY
I
NOTES FOR CHAPTER 4
(APPLICATIONS OF DERIVATIVES)
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BIG FILE: Chapter
4 notes (handwritten). Also, guide
for 4.6: Section 4.6 on
Optimization
COMMENTS ON CH.4 NOTES
Sometimes, it
helps to leave f or f ' in factored form before differentiating; you would
use the Product Rule.
On page 6 of the
4.4/4.5 notes, there's a missing "3" exponent in a denominator near
the bottom.
Technically, you
can have critical numbers (CNs) that correspond to endpoints on a graph, but
you can't have local max or min points at endpoints.
On all three
methods on 4.6 Notes, Page 3, you should note that f is continuous on [0,15].
SMALLER FILES (if you cant get
the big file):
Section 4.1 (pdf): Extrema of
Functions
A
COMMENT ON CRITICAL NUMBERS:
In our major
absolute extrema example in 4.1 (Part D), we looked for critical numbers in the
open interval (-1,8). While critical numbers can, in fact, appear at endpoints
of a restricted interval, local extrema cannot, which is why we look at the
open interval (-1,8) in our example instead of the closed interval [-1,8]. In
our search for absolute extrema, we separated our search for local extrema from
the endpoint issue.
PRECALCULUS NOTES ON DOMAIN AND NONLINEAR INEQUALITIES: Math 141: Section 2.7 in Larson
Section 4.2 (pdf): Mean Value Theorem
(MVT)
Section 4.3 (pdf): First Derivative
Test
Section 4.4 (pdf): f
Section 4.5 (pdf) (fusion of Sections
4.4 and 4.5): Graphing
Web Site: Mathematica engine graphs functions! Lots of info!
http://www.calc101.com/webMathematica/sketch.jsp
Section 4.6 (pdf): Optimization
My guide for
4.6: Section 4.6 on Optimization
Section 4.7 (pdf): More Applications
Section 4.8 (pdf): Newtons Method
Web Site: Calculator for Newton's Method
http://www.math.sc.edu/cgi-bin/sumcgi/Newton.pl
Chapter 4 Notes: 51
pages