Final answer:
To determine concavity by a graph, analyze the shape of the graph and consider the intervals and second derivative.
Step-by-step explanation:
Concavity can be determined by analyzing the shape of a graph. A graph is concave upward if it forms a U-shape, and concave downward if it forms an upside-down U-shape. To identify concavity by a graph, follow these steps:
- Determine the curve of the graph in intervals.
- If the graph is increasing in intervals, it is likely concave upward.
- If the graph is decreasing in intervals, it is likely concave downward.
Verify your findings by considering the graph's second derivative.
- A positive second derivative indicates concave upward.
- A negative second derivative indicates concave downward.
For example, if the graph is increasing in intervals and the second derivative is positive, then the graph is concave upward.