consider the function $\displaystyle f(x)=3x^4+ax^3+bx^2+cx+d$

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

$\displaystyle b.$ there is a third point that is a horizontal tangent. find this point.

c. for all three points, determine whether each corresponds to a local maximum, local minimum, or neither.