Find and graph all critical points of the function
f (x) = 3x2 + 4x + 7
We find the derivative:
f '(x) = 6x + 4.
This is never undefined, and is zero when , so this is our only critical point. In order to have a point to graph, we also need to know the y-value. We plug back into the function:
The exact point on the function is . For the sake of graphing, it's useful to know that
so we know where to put the dot:
Be Careful: When graphing, label points with their exact coordinates. The only reason to find approximate values is so you know where to draw the point.