# Convexity and extreme values

Check that the function:

f(x1, x2, x3) = (x1)^2 + (x2)^2 + (x3)^2 - x1 - x2 - x3

is convex. Find the extreme values of f under the conditions:

(x1)^2 + (x2)^2 = 4, -1 <= x3 <= 1. (x3 goes from -1 to 1)

https://brainmass.com/math/linear-transformation/convexity-extreme-values-207308

#### Solution Preview

see attached

f(x1, x2, x3) = (x1)^2 + (x2)^2 + (x3)^2 - x1 - x2 - x3

is convex. Find the extreme values of f under the conditions: ...

#### Solution Summary

This provides an example of checking that a function is convex and finding extreme values.

$2.19