# How do you find all local maximum and minimum points using the second derivative test given #y=x+1/x#?

##### 1 Answer

Please see the explanation section below

#### Explanation:

**Find the critical numbers for #f#**

The domain of

**Find the second derivative**

**Apply the test**

At

Since the second derivative is negative at the critical number

There is a relative maximum of

I assume that "ralative maximum point" means "point on the graph where

Relative maximum point:

At

Therefore

Again, I assume the requested form for the answer is

Relative minimum point:

**Additional note**

We have finished answering the question, but the answer may look strange to students. (The relative minimum is greater than the relative maximum.)

Here is the graph of

graph{x+1/x [-10.38, 12.12, -7.335, 3.915]}

Note the discontinuity at