Re: Re: max/min of functions
- To: mathgroup at smc.vnet.net
- Subject: [mg27672] Re: [mg27634] Re: [mg27581] max/min of functions
- From: "Mark Harder" <harderm at ucs.orst.edu>
- Date: Sat, 10 Mar 2001 00:50:08 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
oops!
I left out the most important results of this method: the reporting of which
are minima, and which are maxima. The relevant text should read
> Except for the plot this returns
>Out[209]= {x -> 0., x -> 2.}
>Out[211]= {-6., 6.}
>"minima @ {2.}
>"maxima @ {0.}
-mark harder
-----Original Message-----
From: Mark Harder <harderm at ucs.orst.edu>
To: mathgroup at smc.vnet.net
Subject: [mg27672] [mg27634] Re: [mg27581] max/min of functions
> There have been many other solutions, but here is my 2 cents anyway.
>Pick an interesting symbolic expression, one with more than one extremum,
>say x^3 - 3 x^2 + 1 , and execute the following, which solves the equation
>f'(x)=0, then Selects those solutions that have f''(x)<=0 (maxima) and
>f''>=0 (minima):
>
>g = x^3 - 3 x^2 + 1;
>Plot[g, {x, -1, 3}]
>Mrules = Flatten[Solve[D[g, x] == 0., x] ]
>xVals = Map[Replace[x, #] &, Mrules];
>(D[g, {x, 2}] /. x -> #) & /@ xVals
>Print["minima @ ", Select[xVals, (D[g, {x, 2}] /. x -> #) >= 0. &] ];
>Print["maxima @ ", Select[xVals, (D[g, {x, 2}] /. x -> #) <= 0. &] ];
>
> Except for the plot this returns
>Out[209]= {x -> 0., x -> 2.}
>Out[211]= {-6., 6.}
>
> In the event that g(x)=x^3, there are 2 extrema, both =0. and they are
>both minima & maxima, because g''(x)=0 at x=0. When the function is
Sin[x],
>the Solve[] function only generates one solution, but it tells you that
>there may be more solutions.
>
>-mark harder
>
>
>-----Original Message-----
>From: MathBuff <math_buff at REMOVECAPSyahoo.com>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg27672] [mg27634] [mg27581] max/min of functions
>
>
>>After consulting several books and online reference I cannot figure out
how
>>to find the maximum and or minimum values of functions. It seems there
>must
>>be a built in command for this type of thing, but I'll be damned if I can
>>find it. (yes I can do this on a calculator, but I should be able to do
it
>>in mathematica!)
>>
>>here is an example:
>>f(x)=x^2 - 7x -49
>>
>>Also, is there a built in function that will report the vertex in the form
>>x,y ?
>>
>>thanks!
>>
>>Ed
>>(please respond to math_buff at yahoo.com as well as to this newsgroup)
>>