This is the last question in my problem set.

"For the function f(x) = 3x^4 + ax^3 + bx^2 + cx + d,

a. find constants a, b, c, and d that guarantee that the graph of f will have horizontal tangents at (-2, -73) and (0, -9).

b. there is a third point that has a horizontal tangent. Find this point.

c. For all three points, determine whether each corresponds to a relative maximum, a relative minimum, or neither."

My only problem starting this question is what to do with the information given in part a. If someone could provide me a hint, it would be much obliged.