According to the concavity test, what does a negative second derivative indicate?

When performing the concavity test, the second derivative of a function is pivotal in determining the shape of the graph. If the second derivative is negative, it indicates that the graph of the function is concave downwards. This means that the slopes of the tangent lines to the curve are decreasing, and visually, if you were to draw tangent lines, they would lie above the graph itself, suggesting that the curve is bending downwards.

In contrast, a positive second derivative would indicate concave upwards, where the curve bends upward. It’s also important to recognize that a negative second derivative does not imply that the graph is increasing or horizontal; rather, it only informs us about the curvature of the graph, independent of whether the first derivative is positive, negative, or zero. Thus, the correct answer illustrates the relationship between the negative second derivative and the concavity of the graph.