MathDB

Functions question

Source:

April 11, 2017

function

Problem Statement

Define the function

x^2

of the three real variables

x

,

y

,

z

by

m

(

x

,

y

,

z

) = max(

x^2

,

y^2

,

y

),

x

,

y

,

z

∈

R

.
Determine, with proof, the minimum value of

m

if

x

,

y

,

z

vary in

R

subject to the following restrictions:

x

+

y

+

z

= 0,

x^2

+

y^2

+

z^2

= 1.

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