Using the Second Derivative Test to Determine Extrema

This study guide covers the Second Derivative Test for finding local extrema (maxima and minima). It explains how to find critical points using the first derivative, $f'(x)$, and then use the second derivative, $f''(x)$, to classify these points. A positive $f''(x)$ at a critical point indicates a local minimum, while a negative $f''(x)$ indicates a local maximum. The guide includes practice examples and discusses cases where the Second Derivative Test is inconclusive. Finally, it touches upon the relationship between local and global extrema for continuous functions with a single critical point within a given interval.