RE: find out the max ormin of a function
- To: mathgroup at smc.vnet.net
- Subject: [mg41363] RE: [mg41334] find out the max ormin of a function
- From: "David Park" <djmp at earthlink.net>
- Date: Fri, 16 May 2003 06:42:50 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Sabrina,
In making plots I always like to load the following package so I can use the
color names directly.
Needs["Graphics`Colors`"]
Now define your function...
f[x_] := x^2 + 2x + 1
Solve for where the slope is zero and save the solution, which is in the
form of replacement rules. (Much better than actually setting x to some
value.)
xsol = Solve[f'[x] == 0]
{{x -> -1}}
Now let's plot the function and the minimum point. We use xsol, the
replacement rule, to substitute the actual value of x to obtain the point.
Plot[f[x], {x, -2, 2},
Epilog -> {Red, AbsolutePointSize[5], Point[{x, f[x]}] /. xsol}];
Of course, when you are looking for the minimum or maximum in a closed
interval, you also have to consider the case where f'[x] is not zero in the
interval, and so the minimum and maximum will be at the endpoints of the
interval.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: sabrina [mailto:hxs61 at po.cwru.edu]
To: mathgroup at smc.vnet.net
Hi, all:
I just started to learn Mathematica:
I have one function like this: y=x^2+2x+1
How can I find the minimum of this funtion in a range of [-2, 2]? Or put it
in a simple way:
if I know y'=2x+2, how can I use Mathematica to find the minimam? Thanks a
lot
Sabrina