Daniel Dalton <daniel.dalton47 at gmail.com> writes:
> On Sun, Apr 03, 2011 at 07:02:36PM +0100, Leo Butler wrote:
>> < Daniel> 1) Is it possible with maxima to find the local minimums/maximums of a
>> < Daniel> graph, along with the absolute/global minimum and maximum? I'm using the
>> < Daniel> command line interface...
>> <
>> < If you have a symbolic expression, can't you compute the derivative
>> < and use a numerical method to find the zeroes? You can try solve or
>> < mnewton or minpack_solve to find the zeroes.
>
> We haven't covered this in our course yet. I was hoping their was a
> function available like to the other students just to return the
> points... I'll run this by my teacher anyway.
>
Unless the calculators the other students are using do this by working
out a derivative "behind-the-scenes", what they probably do is the
following: Take an evenly spaced list of numbers across the interval in
which you're interested and evaluate the function at each of them. Then
you have an idea of where it's largest. If you want more precision, you
can then choose points closer together near where you think the
minima/maxima are. Obviously this gets done magically behind the scenes,
but it basically works in the same way as drawing a graph and finding
the minima/maxima by eye.
Before other users of the list point it out, this is a lot less
efficient than it could be: if you know the function is smooth (say)
then you can guess a numerical derivative and use that to help you do
Leo's original suggestion.
But anyway, if you ask your teacher about this, try and find out exactly
what method he or she wants you to understand. If he or she just wants
you to get a numerical approximation to the answer, maybe so you get a
feel for a certain function, you could just look at the graph and do it
by eye!
Rupert
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