ind the maximum and minimum values of the function f(x,y,z) = x^2 y^2 z^2 subject to the constraint x^2 + y^2 + z^2 = 400. I am so confused because I got complicated results. Please help!

Question

ind the maximum and minimum values of the function f(x,y,z) = x^2 y^2 z^2 subject to the constraint   x^2 + y^2 + z^2 = 400.  I am so confused because I got complicated results. Please help!

ganeshie8 · Answer

did u use lagrange ?

ganeshie8 · Answer

Clearly the minimum value is 0, occurs when any one of the variable is 0

ganeshie8 · Answer

you can find the maximum value by using symmetry :

max value occurs when $x = y = z$ 
$\large \implies 3x^2 = 400  $

$\large  \implies  x =  \pm \frac{20}{\sqrt{3}}$

anonymous · Answer

I did it but homework page didn'T accepted it. I said (20/sqrt3,20/sqrt3,20/sqrt3)  is maximum points. Website said " This is not a number" .

ganeshie8 · Answer

maximum value : 64000000/27
minimum value : 0

ganeshie8 · Answer

try those^