# Find the equation of the tangent plane to the surface (vector calculus)

• May 10th 2012, 11:39 AM
math254
Find the equation of the tangent plane to the surface (vector calculus)
Find the equation of the tangent plane to the surface z=x(x^2+y)^1/2 at the point (2,5,6)

thank you
• May 11th 2012, 09:31 AM
HallsofIvy
Re: Find the equation of the tangent plane to the surface (vector calculus)
That's a pretty straight forward problem, isn't it? The gradient of f(x, y, z) where [tex]f(x, y, z)= x(x^2+ y^2)^{1/2}- z[tex] is a vector perpendicular to the surface. And once you have vector <A, B, C> perpendicular to the surface at $(x_0, y_0, z_0)$, the tangent plane is given by $A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0$. Have you calculated that?