1. ## Optimization problems

I need some help doing some simple optimization problems. I really don't have any clue how to do them. The concept is completely lost on me.

Find a positive number such that the sum of and is as small as possible.

Can someone give me a simple, step-by-step approach on how to solve these (emphasis on simple)?

2. Originally Posted by G-Rex
I need some help doing some simple optimization problems. I really don't have any clue how to do them. The concept is completely lost on me.

Find a positive number such that the sum of and is as small as possible.

Can someone give me a simple, step-by-step approach on how to solve these (emphasis on simple)?
First put:

$
y=16 x + \frac{1}{x}
$

Then your question is asking you to find $x>0$ which makes $y$ as small as possible. What this is asking is for you to find the minima for $y$ for positive $x$.

The usual way to do this is to find the solutions of:

$
\frac{dy}{dx}=0
$

In your case there is only one solution for positive $x$, and that is the answer you seek.

RonL