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## Homework Statement

Considering the surface of a sphere of radius [itex]1[/itex] with its centre at coordinates

[itex](0,0,0)[/itex].

For the function:

[tex]f(x,y,z) = x^{3} + y^{3} + z^{3}[/tex]

Need to find the following:

(i) All the extrema on the surface which have x, y and z

*all*non-zero simultaneously.

(ii) All the extrema on the surface which have x = 0. [don’t need to say whether the extrema are maxima or minima.]

## Homework Equations

Within the problem question statement and solutions.

## The Attempt at a Solution

.. not really sure how to start this