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:

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

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

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

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

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

RonL