Help with a function and Mean Value Theorem

[alakaboom1]

This is the problem:

Let f be a function defined by f(x)= x[sup:2cejnhgo]3[/sup:2cejnhgo]+ax[sup:2cejnhgo]2[/sup:2cejnhgo]+bx+c and having the following properties:

I) The graph of f has a point of inflection at (0, -2).
II) The average (mean) value of f(x) on the closed interval [0,2] is -3

a) What are the values 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]

I got that a=0 by calculating the second derivative, and then plugging in the inflection point. But I would really appreciate some help with the rest of the problem. Thanks to anyone who can help me out!!

 

[Deleted member 4993]

This is the problem:

Let f be a function defined by f(x)= x[sup:157ob9ny]3[/sup:157ob9ny]+ax[sup:157ob9ny]2[/sup:157ob9ny]+bx+c and having the following properties:

I) The graph of f has a point of inflection at (0, -2).

(0, -2) is on the graph of f(x). What does that tell you about value of 'c'?

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

Please state the definition of average value. Apply it to the above condition.

a) What are the values 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]

Please state the mean value theorem - how that could be applied here?

I got that a=0 by calculating the second derivative, and then plugging in the inflection point. But I would really appreciate some help with the rest of the problem. Thanks to anyone who can help me out!!