The graph is shown above in red. It cuts the x axis at x=0 and 4.
To find the extreme, differentiate y'=12x^2-4x^3. When the gradient is zero we have a turning point, so y'=0 when 3x^2-x^3=0=x^2(3-x), and x=0 and 3. From the graph we can see that x=3 is a maximum and x=0 is a point of inflexion. When x=3, y=108-81=27 so the maximum is at (3,27) and the point of inflexion is (0,0).