A function f(x) with local positive slope implies an increasing
function with x; a negative slope implies a decreasing function with x, and a
zero slope implies a "locally flat" function.. Therefore, a zero slope implies either a minimum or a maximum (it
might also implies an inflection point if the "slope" of the
"slope-function" (second derivative) is zero as well). Finding the maxima and
minima of functions can therefore be done in two steps:
- first calculate the slope of the function
- second solve for the zero
of the slope-function.
This is illustrated in the following Maple worksheet using the Skewed Mexican function
f(x) = x 4 - 3 x 2 - x
which we used previously. The worksheet only uses Maple commands that we have seen previously, and should easily be followed.
The next worksheet does the same for the function
f(x) = sin(x) + cos(x)
in the domain -p to +p.
Section 4.5
Chapter 4
Exercises
TOC
Any questions or suggestions should be directed to
Michel Vallières at vallieres@drexel.edu