Finding Values from points of inflection and avg. mean value

Let F be the function by f(x)=x^3+ax^2+bx+c and having the following properties:

(i) The graph of f has an inflection point at (0,2)

(ii) the average mean value of f(x) on the closed interval [0,-2] is -3

a.) Determine the value of a, b, and c

b.) Determine the value of x that satisfies the conclusion of the mean value theorem for f on the closed interval [0,3]

Okay so I found out that both a and b equals -1 based on the properties, but I cant fins out what c is and I'm stuck. Help please?