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

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

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

BUT... is a POSITIVE number (given in the question), so , the other number being .