Relative Extrema and More Analysis of Functions Section 5.2

Critical Points vs. Stationary Points Critical Point – A point in the domain of f where f where f has a horizontal tangent line or is not differentiable Stationary Point – A point on the graph where the

1st Derivative Test If extending left from and extending right from , then f has a relative maximum at If extending left from and extending right from , then f has a relative maximum at If has the same sign as it extend in either direction, then f does not have a relative extrema at

In other words….. If a function increases from the left and decreases to the right of , then there is a relative maximum at the point If a function decreases from the left and increases to the right of , then there is a relative minimum at the point If the sign of the derivative does not change, then the function either increases or decreases and does not have a relative max or min

Increase: _________ Stationary Points:________ Decrease: _________ Inflection Points: ________ Concave Up: _________Rel. Maximum: _________ Concave Down: _______Rel. Minimum: _________

Increase: _________Stationary Points:________ Decrease: _________Inflection Points: ________ Concave Up: _________Rel. Maximum: _________ Concave Down: ________Rel. Minimum: _________

Examples with Graphs Give the relative max, min, and inflection points 4 2 3

Practice pg. 287 (7, 9, 15 - 18, 27, 28, 31 – 34)