Question

Find the tangent plane for the function f(x, y) = x^2 + y^3 at the point (2, 1).​

Answer 1

Compute the gradient of
`f` at (2, 1).

`\\abla f(x,y) = \langle 2x, 3y^2 \rangle \implies \\abla f(2, 1) = \langle 4, 3 \rangle`

Then the tangent plane to
`f(x,y)` at (2, 1) has equation

`T(x,y) = f(2, 1) + \\abla f(2,1) \cdot \langle x-2, y-1\rangle = \boxed{4x + 3y - 6}`