The first derivative test is a method used in calculus to determine the local maxima and minima of a function. By analyzing the sign of the first derivative, f'(x), we can identify where the function is increasing or decreasing. If the derivative changes from positive to negative at a point, that point is a local maximum. Conversely, if it changes from negative to positive, it indicates a local minimum. To apply the first derivative test, one must first find the critical points where f'(x) = 0 or where the derivative does not exist. By evaluating the sign of the derivative in the intervals around these critical points, we can conclude the nature of each point, helping to understand the overall behavior of the function.