Hey i need to complete the following exam questions for my tutor for tomorrow but i am having trouble understanding them:

1. Show that $\displaystyle x^2+x+1>0$ for all values of x. (3 marks)

For questions such as these am i supposed to use proof or what... im just not sure how to approach such a simple equation.

The 2nd question is a harder question involving calculus:

2. The curve C has the equation $\displaystyle y=\frac{x}{9+x^2}$

Find the coordinates of the turning points of C. (6 marks)

I have got so far on the 2nd question:

$\displaystyle y=\frac{x}{9+x^2}$

Using quotient rule:

$\displaystyle \frac{d}{dx}(\frac{x}{9+x^2})=\frac{1(9+x^2)-x(2x)}{(9+x^2)^2}$

$\displaystyle =\frac{9+x^2-2x^2}{(9+x^2)^2}$

$\displaystyle =\frac{9-x^2}{(9+x^2)^2}$

In order to complete the question i must know some values of x or y to substitute in order to find the turning points, but i am not sure how i can get them with such little information.

I would be grateful if someone could show me how to complete the question with full workings.

Thanks in advance to anyone who helps out.