Consider the function f(x)=3x3+2x2+4. For what values of k does the Intermediate Value Theorem tell us that there is a c in the interval [0,1] such that f(c)=k?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.