What is the equation of the tangent plane?

Question

Find an equation of the tangent plane P = (2, 3, 3/√e) to the given surface. 7x^2 + z^2 e^y-x = 37

equation = ?

Answer 1

Let F= 7x² +z²e^y-x -37 =0 So now F_x =14x -z²e^y-x F_y =z²e^y-x F_z =2ze^y-x. Using the point P(2,3,3/e^1/2) in the expressions for F_x, F_y , F_z gives (17,9,6e^1/2). So the equation of the plane becomes 17(x-2) + 9(y-3) + 6e^1/2(z-3/e^1/2) =0. Simplifying this equation gives 17x +9y +6e^1/2z = 79.