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### Finding the Critical Point

```
Date: 05/09/2000 at 00:56:35
From: Veerawong Pipithsuksunt
Subject: Calculus - Critical point

Dear Dr. Math,

Find the critical point of

f(x,y,z,t) = (x^2)*(y^2)*(z^2) + (t^2)*(x^2) + 3x

and determine whether the point is a maximum, minimum, or saddle
point.

I can not find the critical point...

Thank you,
Veerawong
```

```
Date: 05/09/2000 at 08:23:47
From: Doctor Jerry
Subject: Re: Calculus - Critical point

Hi Veerawong,

I think that you cannot find a critical point because there is no
critical point; that is, a point (x,y,z) for which each of the
partials are 0.

(<> means not equal to)

t <> 0 is not possible because if this were true, then x = 0
(because t*x^2 = 0); but this is impossible because
3 + 2t^2*x + 2x*y^2*z^2 = 0.

t = 0 is not possible because if you check all the cases, each is
impossible. For example, with t = 0, then consider x <> 0 and
x = 0 cases; in the first, y = 0, but this cannot be because
3 + 2x*y^2*z^2 = 0. And so on.

- Doctor Jerry, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Calculus

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