Bard Math 212 - Tangent Planes

660 days ago by ethan

Tangent Plane to a Surface in \mathbb{R}^3

The surface, in blue, is the graph of z = x^2 + y^2.

The point of tangency, in red, is (1, 2, 5).

The tangent plane, in yellow, is z = 2x + 4y - 6, in yellow.
x, y = var('x,y') P = plot3d(x^2 + y^2, (x,-4,4), (y,-4,4), opacity=0.7) Q = plot3d(2*x + 4*y - 6, (x,-4,4), (y,-4,4), opacity=0.7, color='yellow') S = sphere((1,2,5),size=0.1, color='red', aspect_ratio=1) P + Q + S