Re: find the maxima in a function

• To: mathgroup at smc.vnet.net
• Subject: [mg97098] Re: [mg97052] find the maxima in a function
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 5 Mar 2009 04:55:00 -0500 (EST)
• References: <200903041210.HAA27070@smc.vnet.net>

```f[x_] := 1/(8*(Pi*t)^(3/2))*Exp[(-(x^2 + y^2 + z^2)/4*t)]

D[f[x], x]

-((E^(1/4 t (-x^2 - y^2 - z^2)) x)/(16 \[Pi]^(3/2) Sqrt[t]))

As you can see, the denominator is zero if and only if x == 0, and at that
point, the second derivative is

D[f[x], {x, 2}] /. x -> 0

-(E^(1/4 t (-y^2 - z^2))/(16 \[Pi]^(3/2) Sqrt[t]))

(negative). Unless Sqrt[t] is taken negative somehow.

Bobby

On Wed, 04 Mar 2009 06:10:25 -0600, Oliver <sch_oliver2000 at yahoo.de> wrote:

> Hallo,
> how can one find the maxima by using mathematica for the following
> function:
>
> f[x_] := 1/(8*(Pi*t)^(3/2)) * Exp[(-(x^2 + y^2 + z^2)/4*t)]
>
> i mean, the first derivation equal Zero.
> Oli.
>

--
DrMajorBob at bigfoot.com

```

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