Hey guys I have just started learning mathematica and I was wandering if someone could confirm if I did the following correct:(adsbygoogle = window.adsbygoogle || []).push({});

Question:

Find the tangent plane to the surface z = 2x^2 -y^2 at the point (2,1). Plot the tangent plane and the surface on the same graph. Change th eviewpoint to show the tangent plane clearly.

Solution:

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

point1 = 2;

point2 = 1;

f[x_, y_] = 2x^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)"}]

Thanks in advance

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# Find the tangent plane to the surface in Mathematica

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