- #1

- 3

- 0

## Main Question or Discussion Point

The goal is to plot both the surface graph of the function and the tangent plane to the surface on one plot. There are two functions I believe I'm having issues with:

f(x,y) = cos(x+y)exp(x^2 - y^2) @ point (0.5,-0.5)

&

f(x,y) = sin(exp(xy)) @ point (1,1)

My code for the two are as follows respectively:

Clear[f,x,y,fx,fy,point1,point2]

point1=0.5;

point2=-0.5;

f[x_,y_]=cos(x+y)exp((x^2) - (y^2));

fx[x_,y_]=D[f[x,y],x];

fy[x_,y_]=D[f[x,y],y];

T[x_,y_]:=f[point1,point2]+fx[point1,point2](x-point1)+fy[point1,point2](y-point2)

T[x,y]

Clear[G1,G2];

G1=Plot3D[f[x,y],{x,-2,10},{y,-4,4}]

G2=Plot3D[T[x,y],{x,-2,10},{y,-4,4}]

Show[G1,G2,ViewPoint -> {0,-2,0.3},AspectRatio -> 1,AxesLabel -> {"x","y","f(x,y)"}]

for the second:

Clear[f,x,y,fx,fy,point1,point2]

point1=1;

point2=1;

f[x_,y_]= sin(exp(xy));

fx[x_,y_]=D[f[x,y],x];

fy[x_,y_]=D[f[x,y],y];

T[x_,y_]:=f[point1,point2]+fx[point1,point2](x-point1)+fy[point1,point2](y-point2)

T[x,y]

Clear[G1,G2];

G1=Plot3D[f[x,y],{x,-2,10},{y,-4,4}]

G2=Plot3D[T[x,y],{x,-2,10},{y,-4,4}]

Show[G1,G2,ViewPoint -> {0,-2,0.3},AspectRatio -> 1,AxesLabel -> {"x","y","f(x,y)"}]

I believe the outputs I'm getting are wrong. For the cos one it just plots a flat plane at 0. For the second one there isn't any plot. I've changed around the intervals and viewpoints, but still nothing shows up. Just looking for a little insight into the issue. thanks!

f(x,y) = cos(x+y)exp(x^2 - y^2) @ point (0.5,-0.5)

&

f(x,y) = sin(exp(xy)) @ point (1,1)

My code for the two are as follows respectively:

Clear[f,x,y,fx,fy,point1,point2]

point1=0.5;

point2=-0.5;

f[x_,y_]=cos(x+y)exp((x^2) - (y^2));

fx[x_,y_]=D[f[x,y],x];

fy[x_,y_]=D[f[x,y],y];

T[x_,y_]:=f[point1,point2]+fx[point1,point2](x-point1)+fy[point1,point2](y-point2)

T[x,y]

Clear[G1,G2];

G1=Plot3D[f[x,y],{x,-2,10},{y,-4,4}]

G2=Plot3D[T[x,y],{x,-2,10},{y,-4,4}]

Show[G1,G2,ViewPoint -> {0,-2,0.3},AspectRatio -> 1,AxesLabel -> {"x","y","f(x,y)"}]

for the second:

Clear[f,x,y,fx,fy,point1,point2]

point1=1;

point2=1;

f[x_,y_]= sin(exp(xy));

fx[x_,y_]=D[f[x,y],x];

fy[x_,y_]=D[f[x,y],y];

T[x_,y_]:=f[point1,point2]+fx[point1,point2](x-point1)+fy[point1,point2](y-point2)

T[x,y]

Clear[G1,G2];

G1=Plot3D[f[x,y],{x,-2,10},{y,-4,4}]

G2=Plot3D[T[x,y],{x,-2,10},{y,-4,4}]

Show[G1,G2,ViewPoint -> {0,-2,0.3},AspectRatio -> 1,AxesLabel -> {"x","y","f(x,y)"}]

I believe the outputs I'm getting are wrong. For the cos one it just plots a flat plane at 0. For the second one there isn't any plot. I've changed around the intervals and viewpoints, but still nothing shows up. Just looking for a little insight into the issue. thanks!