Compute the tangent plane to the graph of f(x,y)=2x^2+y^2 over the point (1,0) by the following method. A) Hold y fixed at y=0 and consider the space curve r1(x) = , parametrized by x. Find a tangent vector v1 of r1 at x=1. Use the tangent vector to find the tangent line of r1 at x=1. B) Hold x fixed at x=1 and consider the space curve r2(y)=, parametrized by y. Find the tangent vector v2 or r2 at y=0. use your tangent vector to find the tangent line of r2 at y=0. C) Find the plane containing the two tangent lines you found in part a and b.

Question

Compute the tangent plane to the graph of f(x,y)=2x^2+y^2 over the point (1,0) by the following method. A) Hold y fixed at y=0 and consider the space curve r1(x) = , parametrized by x. Find a tangent vector v1 of r1 at x=1. Use the tangent vector to find the tangent line of r1 at x=1. B) Hold x fixed at x=1 and consider the space curve r2(y)=<1,y,f(1,y)>, parametrized by y. Find the tangent vector v2 or r2 at y=0. use your tangent vector to find the tangent line of r2 at y=0. C) Find the plane containing the two tangent lines you found in part a and b.