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Math Help - 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 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
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