Thread: Understanding range in functions of 2 variables

1. Understanding range in functions of 2 variables

I am having trouble understanding the range in f(x,y)=4x^2+9y^2. The answer is z>=0 but my book is not helping me understand how to find this. Can someone please help explain this to me? Thank you.

2. Originally Posted by cowboys111
I am having trouble understanding the range in f(x,y)=4x^2+9y^2. The answer is z>=0 but my book is not helping me understand how to find this. Can someone please help explain this to me? Thank you.
we have $z = 4x^2 + 9y^2$

now, $4x^2 \ge 0$ for all $x$ and $9y^2 \ge 0$ for all $y$. 0 is the minimum for both of these

thus, $z \ge 0 + 0 = 0$