# Thread: Minimum value of function

1. ## Minimum value of function

Hi,
I need to tell what's the minimum value of this function:

$f(x)=\sqrt{x+2(1+ \sqrt{x+1})} + \sqrt{x+2(1-\sqrt{x+1})}$

It's probably 2, but I have no idea how to prove it.

2. Originally Posted by bobb12
Hi,
I need to tell what's the minimum value of this function:

$f(x)=\sqrt{x+2(1+ \sqrt{x+1})} + \sqrt{x+2(1-\sqrt{x+1})}$

It's probably 2, but I have no idea how to prove it.
Here are the steps to solve this problem:

First find the domain of the function.

work NOT shown it is $[0,\infty)$

So the domain has one boundary point.

2nd find the derivative and set it equal to zero. (there are no solutions,again work not shown)

So the global minimum must occur at the boundary point. $x=0$

and $f(0)=2$

3. Originally Posted by TheEmptySet
Here are the steps to solve this problem:

First find the domain of the function.

work NOT shown it is $[0,\infty)$

So the domain has one boundary point.

2nd find the derivative and set it equal to zero. (there are no solutions,again work not shown)

So the global minimum must occur at the boundary point. $x=0$

and $f(0)=2$
Thanks a lot, but could You tell me how i can find the derivative of this function?