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A Surface and its Tangent Plane

We need plots

> with(plots):

Look at the function f(x,y)=x^2 + y^2

> f:=x^2 + y^2;

Set S to be the surface

> S := plot3d(f,x=0..2,y=0..2,color='red'):

To get the equation of the tangent plane, we need to find
the partial derivatives of f

> dfdx:=diff(f,x); dfdy:=diff(f,y);

Let's look at the tangent plane at (x,y)=(1,1):
The equation of the tangent plane is

z = f(1,1) + dfdx(1,1) * (x-1) + dfdx(1,1) * (y-1)

> z := subs(x=1,y=1,f)+subs(x=1,y=1,dfdx)*(x-1)+subs(x=1,y=1,dfdy)*(y-1);

Call the tangent plane P

> P := plot3d(z,x=0..2,y=0..2,color='yellow'):

Show the surface and its tangent plane on the same graph

> display3d({S,P});

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