Hi,
I need to tell what's the minimum value of this function:
$\displaystyle f(x)=\sqrt{x+2(1+ \sqrt{x+1})} + \sqrt{x+2(1-\sqrt{x+1})}$
It's probably 2, but I have no idea how to prove it.
Thanks in advance
Here are the steps to solve this problem:
First find the domain of the function.
work NOT shown it is $\displaystyle [0,\infty)$
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. $\displaystyle x=0$
and $\displaystyle f(0)=2$