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## Intervals of Concavity

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**Unit 4**Intervals of Concavity**Definition**A graph is concave up if it forms a parabola that opens upward A graph is concave down if it forms a parabola that opensdownward Aninflection point is a point where a graph switches concavity**Example graphs**Concave up Concave down**Example of Inflection Point**Point of inflection is at (0,0). This is where the concavities change from up ward to downward. (- ) 8 8 Concave up: , 0) Concave down: ( 0, Point of Inflection: (0,0)**Procedure**Find the second derivative Find the critical numbers Where f”(x)=0 Values of x that make f(x) or F”(x) undefined Place those values on a number line Test a value in each interval in the second derivative Concave up where f”(x) is positive Concave down where f”(x) is negative Write the intervals**Examples**Concave up: (-1/4, Concave down: ( ,-1/4) Infection point: (-1/4, 29/8) ) 8 8 -1/4