Hello, I've asked a couple of my classmates and even another calculus teacher for help but have had no success getting anywhere with this problem. I'm hoping someone can help me figure this out (my calculus teacher comes up with his own problems, this was not out of a book and does not give any help with the homework problems he assigns.)

Find a,b,c and d such that p(x)= ax^3 + bx^2 + cx+ d satisfy the following conditions:

g(0)=3,extrema at x=1.263762616,x=-.2637626158, inflection point at x=.50, f''< 0 when x<0.5, f'' >0 when x>0.5