6.5 Using derivatives in graphing

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Presentation transcript:

6.5 Using derivatives in graphing Let 𝑔 𝑥 = 𝑥 3 −3 𝑥 2 −9𝑥+22 Find the intervals on which 𝑔 is increasing and on which 𝑔 is decreasing. Use the information to graph.

𝑔 𝑥 = 𝑥 3 −3 𝑥 2 −9𝑥+22 Find the derivative (this will give you the x-values of the extremes) Find the y-coordinates of those extremes By plugging in particular x-values within the intervals created by the zeros, determine whether the graph is increasing (+ derivative) or decreasing (- derivative) By looking at the behavior of the graph around your stationary points, determine whether an extreme point (relative or absolute) actually exists there.