Parabola(?) Question

2.Give a neat sketch of S=x+\frac{144}{x} for x>0. This is the part I have trouble- i cant tell what sort of a graph it is. The answers show a parabola as the solution but I don't know why it is a parabola

$S=x+\frac{144}{x}$
$Sx=x^2+144$
$x^2-Sx+144=0$

Is it apparent now why this is a parabola? Remember, the SUM is a fixed number, so it can be treated as a constant (Giggle)

3. What is the size of two numbers which will make the value of S least. (again, cant do this one)

To make S the least, it's the same as MINIMISING S, minimisation problems are achieved through calculus, and is obtained by solving $\frac{dS}{dx}=0$

$S=x+\frac{144}{x}$

$\frac{dS}{dx}=0$
$1-\frac{144}{x^2}=0$
$x^2-144=0$
$x^2=144$
$x=\pm12$

BUT... $x$ is a POSITIVE number (given in the question), so $x=12$ , the other number being $\frac{72}{x}=6$ .