Question

I need to find the tangent plane at (-1,2,4), and I have a function z = 4x^2-y^2+2y.

Answer 1

Suppose f has a continuous partial derivatives. An equation of the tangent plane to the surface
\[z=f(x,y)\] at the point
\[P(x_0,y_0,z_0)\]is
\[z−z_0=f_x(x_0,y_0)(x−x_0)+f_y(x_0,y_0)(y−y_0)\]

Answer 2

Ohh right, So I find the partial derivatives first, and insert.

Answer 3

is it correct that i've gotten f_x(x_0,y_0) = 8x and f_y(x_0,y_0) = -2y+2 ??

Answer 4

Yeap, :)