First Derivative Test for Local Extrema. If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point.
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. Hence First and second derivative use for properties of curve.
Derivative
