QuestionFind the equation of the tangent plane to the surface determined by $$x^{4} y^{4}+z-45=0$$ at $x=2, y=3$. $$z=$$
Submit answer Next item

Studdy Solution
Use the point $(2, 3, -1251)$ and the normal vector $\langle 2592, 1728, 1 \rangle$ to write the equation of the tangent plane.
The equation of the tangent plane is given by:
$$2592(x - 2) + 1728(y - 3) + 1(z + 1251) = 0$$
Simplify:
$$2592x - 5184 + 1728y - 5184 + z + 1251 = 0$$
Combine constants:
$$2592x + 1728y + z - 9117 = 0$$
The equation of the tangent plane is:
$$\boxed{2592x + 1728y + z = 9117}$$