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Thread: Understanding range in functions of 2 variables

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    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.
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    Quote Originally Posted by cowboys111 View Post
    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 $\displaystyle z = 4x^2 + 9y^2$

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

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