Fermat's Theorem (stationary Points) - Fermat's Theorem

Fermat's Theorem

Let be a function and suppose that is a local extremum of . If is differentiable at then .

Another way to understand the theorem is via the contrapositive statement:

• If is differentiable at, and
• ,
• then is not an extremum of f.

Exactly the same statement is true in higher dimensions, with the proof requiring only slight generalization.