Need help only with part (b) and (c)

(a) Use properties of quadratic functions to prove that 3x2(x+1)2 for all real x4. (b) Use mathematical induction and the inequality from part (a) to prove that 3n2n+3n2 for all integers n4 (c) Let g(n)=2n+3n2 and h(n)=3n. Using the inequality from part (b), prove that g(n)=O(h(n)). You need to give a rigorous proof derived directly from the definition of the O-notation, without using any theorems from class. (First, give a complete statement of the definition. Next, show how g(n)=O(h(n)) follows from this definition.)