Final answer:
The statement is true; the second derivative test is used to find and classify local maxima and minima in a function by examining the concavity at points where the first derivative is zero.
Step-by-step explanation:
True: The second derivative test is indeed a method used in calculus to find and classify local maxima and minima of a function. This test involves taking the second derivative of the function, which gives us information about the concavity of the graph. If the second derivative at a point where the first derivative is zero (i.e., a potential maximum or minimum) is negative, this suggests that the graph is concave down at that point, and hence it is a local maximum. Conversely, if the second derivative is positive, the graph is concave up, and the point is a local minimum.
If the second derivative is zero, the test is inconclusive, and we may need to use other methods to determine whether the point is a maximum, minimum, or neither. Local maxima and local minima are important in various fields as they can represent critical points in a given context—like the highest or lowest values of a sales graph, the peaks and troughs in a physical wave, or the optimum points in an engineering problem.