Re: max/min of functions
- To: mathgroup at smc.vnet.net
- Subject: [mg27634] Re: [mg27581] max/min of functions
- From: "Mark Harder" <harderm at ucs.orst.edu>
- Date: Fri, 9 Mar 2001 02:35:47 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
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
Subject: [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)
>