# How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for # f (x) = x + 4/x #?

##### 1 Answer

You determine studying the derivative.

#### Explanation:

You have to evaluate the derivative of the function.

The derivative is the value of the slope, so when the derivative is positive the function is increasing, when it is negative the function is decreasing and when it is zero you have a maximum, a minimum or an horizontal flex.

So let's calculate the derivative

Its graph is in figure

graph{1-4/x^2 [-10.17, 9.83, -4.92, 5.08]}

When

To verify this we can see the plot of

graph{x+4/x [-20.17, 19.83, -9.92, 10.08]}