Verified Answer :

The answer is \(f(3)=3,408.\)

To solve this problem, just plug \(3\) into the function and simplify.

\(f(x) = 5x^6 - 3x^5 + 6x^4 +6 \\ f(3) = 5(3)^6 - 3(3)^5 + 6(3)^4 +6 \\ = 5(729) - 3(243) + 6(81) + 6 \\ = 3645 - 729 + 486 + 6 \\ = 3408\)