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Homework Statement
f(x,y,z) = 4x^2 + y^2 + 9z^2
another one is xy+z^2
how do u draw level curves and graphs for these?
Homework Equations
The Attempt at a Solution
Just need somewhere to start
Thanks
The problem with "drawing graphs" for these is that you need three orthogonal axes for the independent variables, x, y, and z, and an axes perpendicular to all of those for the function value, f. That is, you will need a four dimensional graph.Homework Statement
f(x,y,z) = 4x^2 + y^2 + 9z^2
another one is xy+z^2
Level curves will help you reduce a dimension by treating the function value as a constant. That is, the level curves (more correctly "level surfaces") for for f(x,y,z)= 4x^2+ y^2+ 9z^2 will be the three dimensionl graphs 4x^2+ y^2+ 9z^2= C for different values of C. Those will be a number of ellipsoids, of different sizes, one inside the other.how do u draw level curves and graphs for these?
Homework Equations
The Attempt at a Solution
Just need somewhere to start
Thanks