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Tangent plane in 3D - Printable Version

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Tangent plane in 3D - Tonig00 - 12-27-2018 07:00 AM

I would like to draw a tangent plane to a function in 3D APP.

I work in CAS mode in the following example:
For example FZ1(X,Y)=X^1/3 * Y^1/3:
I introduce this equation in "Symbolic View" in de 3D APP. It draws it correctly when I press "Plot".

Then I introduce the plane equation in a point (for example (1,1)):
FZ2(X,Y)=FZ1(1,1)+dFZ1(X,Y)/dX * (X-1) + dFZ1(X,Y)/dY * (Y-1)

When I press Plot it does not draw the plane.

I have tried to derivate it directly dFZ1(X,Y)/dX and it gave me 0,

Could somebody give me an idea to how to trace that plane?

Thanks very much


RE: Tangent plane in 3D - toshk - 12-27-2018 06:26 PM

CAS; type
FZ1(x,y) enter
// gradient; numerical del operator
nDeriv(x^(1/3)*y^(1/3),{x,y}) enter;

//for Partial derivative do this instead
nDeriv(x^(1/3)*y^(1/3),x) enter;
nDeriv(Ans,y) enter;

save your appropriate ans(del or Partial your choice) in say FZ2; change x,y to X,Y iferr
do the steps...
doing this FZ2:= nDeriv(x^(1/3)*y^(1/3),{x,y}) enter; might not work;

applies to Function App too;