On the Same Coordinate Axes, Sketch the Graphs (As Accurately $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3$

question 130

Essay

On the same coordinate axes, sketch the graphs (as accurately as possible) of the functions $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3$ and $g ( x ) = - 4 x ^ { 2 } + 3 x + 3$ . Based on your sketch, how many points do the graphs appear to intersect? Find the coordinates of all intersection points.