1. ## differentation question

Hi everyone i was just wondering if anyone could help with this differentiation question it is :

Use differentitation to find the coordinates of the stationary points on the curve.
Y= x + 4/x
And determine whether each stationary point is a maximum point or minimum point.
Find the set of values of x for which y increase as x increases.

Thanks Gracey

Even if you can help with a small part of the question i would be grateful

2. I think this is what you mean:

$\displaystyle y=x+\dfrac{4}{x}$
$\displaystyle \dfrac{dy}{dx}=1-\dfrac{4}{x^2}$
$\displaystyle 0=1-\dfrac{4}{x^2}$
$\displaystyle x=\pm2$

Look at the sign of the derviative in the interval $\displaystyle (-\infty, \infty)$

you will find that it is a local max at $\displaystyle x=-2$ and local min at $\displaystyle x=2$

Therefore the function is increasing from $\displaystyle (-\infty,-2)$ and $\displaystyle (2,\infty)$ and decreasing on $\displaystyle (-2,0), (0,2)$

3. thankyou so much that is excellent.