In this section, you will see how locating the intervals in which increases or decreases can be used to determine where the graph of a function is curving upward or curving downward. - If an interval is curving (or bending) upward, it is considered concave upwards. Its second derivative along this interval will be positive.
- If an interval is curving (or bending) downward, it is considered concave downwards. Its second derivative along this interval will be negative.
- If an interval is not curving at all, then its second derivative is zero.
**Key Terms**- concavity
- inflection points
- Second Derivative Test
Essential Questions- How are derivatives used to determine where a function is concave upward, concave downward, or neither?
Practice ProblemsExtra Practice |