Final answer:
To determine concavity, analyze the graph for shapes like cups (concave upward) or caps (concave downward), or calculate the second derivative—positive for concave upward and negative for concave downward intervals.
Step-by-step explanation:
The question pertains to determining where a function is concave upward and where it is concave downward. To identify these regions, one can either analyze the function's graph or calculate its second derivative. For example, if a graph of a function shows a region where the curve is opening upwards, like the shape of a cup, that region is concave upward. Similarly, if the graph shows a region where the curve is opening downwards, that region is concave downward. Alternatively, taking the second derivative of the function provides a mathematical method for determining concavity: if the second derivative is positive, the function is concave upward in that interval; if it is negative, the function is concave downward.