Find all values of x where f ′(x) = 2 given
Since f(x) is cubic, f '(x) will be quadratic. Predict how many solutions there will be to f '(x) = 2.
The blue curve shows f '(x) intersecting the dotted line y = 2. Do your solutions look correct?
Use the Power rule to find f '(x).
Set f '(x) = 2, and solve for x.
Use the eTool below to explore the graph of f(x).
Click the link at right for the full version of the eTool: Calc 3-122 HW eTool