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Math Help - Level Curves

  1. #1
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    Unhappy Level Curves

    Function: z=f(x,y)=5-x^2-y^2
    How would you draw a contour plot and label the level curves for z=0, z=1, z=2, z=3, z=4, z=5? Also, how do you find out what the largest and smallest z-values are? Would the smallest be z=0 and the largest be z=5?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    for the level curves z = c = 5- x^2 -y^2

    x^2 + y^2 = 5 - c are concentric circles of radius sqrt(5-c)

    for c= 0 ,1,2,3,4,5
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  3. #3
    Senior Member
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    Quote Originally Posted by eri123 View Post
    Function: z=f(x,y)=5-x^2-y^2
    How would you draw a contour plot and label the level curves for z=0, z=1, z=2, z=3, z=4, z=5? Also, how do you find out what the largest and smallest z-values are? Would the smallest be z=0 and the largest be z=5?
    because x^2 + y^2 \geq 0 for all x,y, then the largest value of z = 5 - (x^2 + y^2) is 5 and the smallest is - \infty
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