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For each graph below: 

  1. Trace the graph onto your paper and write a slope statement for .

  2. Sketch the graph of using a different color.

  1. Decreasing line, labeled, f of x, passing through the points (0, comma 4), & (2, comma 3).

  1. Curve primarily in first quadrant, x axis scaled from 0 to 4, labeled, f of x, coming from lower left, turning at the y axis, at about 3, changing concavity at about (1, comma 2), turning up at about, (3, comma 1), continuing up & right.

  1. Downward parabola labeled, f of x, vertex at about (3, comma 3), passing through the x axis between 1 & 2, & between 4 & 5.

Slope statements should tell a story, starting at the left side of the graph and ending at the right side. There should be a description of where the function is increasing or decreasing and how the rate at which it is increasing or decreasing is changing.

Use your slope statements to sketch the derivative graphs. Pay attention to whether the slope has positive or negative values. Also pay attention to whether those values are increasing or decreasing.