Finding a real number c for polynomial (proof) The question is to find a real number c for which $ x\ge c%+$ implies $$x^4-4x^3+7x-9 \ge1000$$.
I was given the hint that $x>10$, then $4x^3<0.4x^4$, so $x^4-4x^3>0.6x^4$.
Problem is, I'm not understanding this line of reasoning, particularly how x>10 goes to the next step involving the $0.4x^4$.

If $x > 10$ then $0.4x > 4$ and so $4x^3 < (0.4x)x^3 = 0.4x^4$. Therefore $x^4 - 4x^3 > x^4 - 0.4x^4 = 0.6x^4$.
Furthermore, if $x > 10$, then $7x - 9 \geq 7(10) -9 = 61$. Therefore, if $x > 10$, $x^4 - 4x^3 + 7x - 9 > 0.6x^4 + 61$. So how big should $x$ be so that $0.6x^4 \geq 1000?$
