Im trying to check my answers to a problem, and in the past i've used a 3d grapher to graph functions like f(x,y) = whatever. but now i need to find a tangent plane to a surface at a point. the surface is: x^{2}y+y^{2}z-z^{2}x=1 but i dont know how to go about graphing something expressed that way. are there different names to these types of graphs? are there programs that will graph things expressed other than z=[stuff w/ x and y]?
If you find the tangent in orthogonal directions you should be able to use the tangent vectors in both directions to compute the normal and hence the tangent plane. Have you studied multivariable and vector calculus?
im in a multivariable calculus class right now, and the point given was (2,3,-1) what i did was take the partials w/ respect to x y and z. then i plugged in the values at that point. then i plugged that into the equation f_{x}(x-x_{0})+f_{y}(y-y_{0})+f_{z}(z-z_{0})= 0 i ended up getting 11x-2y+13z = 3 but my question was mainly about the notation of the equations. some expressed in terms of z or f(x,y). this one is given as a function of (x,y,z) = constant i guess its like comparing graphs like x^{2}+y^{2}=1 to f(x)= y= 3x+1 its harder to graph the first one on a calculator because its not a function of x. are there names for different forms of the equations? and also, is there a good graphing program to graph those kinds of surfaces.