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## Homework Statement

Why is

[tex] \nabla f = \lambda \nabla g [/tex]

where f is the function you want to find the extrema of and g is the contraint?

Also how would you identify the above in the following

Determine the least real number M such that the inequality

[tex]

|ab(a^2-b^2) + bc(b^2-c^2) + ca(c^2-a^2)|\le M(a^2 + b^2 + c^2)^2[/tex]

holds for all real numbers a, b and c.

## The Attempt at a Solution

It is the first part of the problem which I cannot do so there is no working to show

You have to minimise M but subject to what? Also, there is no explicit definition for M, only the inequality.

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