Let $x, y \in \mathbb{R}$, $a, b, c$ are three real parameters with $c\neq 0$. Find the maximum and minimum of $\dfrac{ax+by+c}{\sqrt{x^2+y^2+1}}$
This is quite complicated if I calculate the derivative. Is there any other ways? Please help me.
Thanks.
I know that some people has voted my question down, I know how to use Cauchy-Schwarz inequality, but this only gives me the maximum, not the minimum. I'm not good at this kind of math, so, instead of voting down, please explain for me.