The first derivative test is a way to find if a critical point. Critical point is a relative minimum or maximum. The first derivative is negative to the left of the critical point, and positive to the right of it, it is a relative minimum.
Second Derivative Test. 1. If , then has a local minimum at . 2. If , then has a local maximum at . The extremum test gives slightly more general conditions under which a function with is a maximum or minimum.
If is a two-dimensional function that has a local extremum at a point and has continuous partial derivatives at this point
