Step 1 :The function \(f(x)=2(x-4)^{4}\) is a polynomial function of degree 4. It is a transformation of the parent function \(f(x)=x^{4}\), where the graph is shifted 4 units to the right and vertically stretched by a factor of 2.
Step 2 :The function has only one zero at x=4, because \((x-4)^{4}\) equals zero only when x=4.
Step 3 :The function has no relative maximums or minimums, because it is always increasing for x>4 and always decreasing for x<4.
Step 4 :Both ends of the graph of the function go up, because as x approaches positive or negative infinity, the value of the function also approaches positive infinity.
Step 5 :Therefore, the correct statements are C and D.
Step 6 :Final Answer: \(\boxed{\text{C, D}}\)