Finding the Critical PointDate: 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/ |
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