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In this section, you will see how locating the intervals in which the derivative of a function 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.
Essential Questions
Essential Questions
How are derivatives used to determine where a function is concave upward, concave downward, or neither?
How are derivatives used to determine where a function is concave upward, concave downward, or neither?
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