Question

Find the equation of the tangent plane to the surface 2(x - 5)² (y - 6)² (z - 5)² = 10 at the point (6, 8, 7).

Answer 1

To find the equation of the tangent plane to the given surface at a point, we can start by finding the partial derivatives with respect to x, y, and z. By substituting the coordinates of the point into the equation and simplifying, we can determine the equation of the tangent plane.

Step-by-step explanation:

To find the equation of the tangent plane to the surface, we can first find the partial derivatives with respect to x, y, and z. Taking the partial derivative with respect to x gives us:

2(2(x - 5))(y - 6)²(z - 5)² = 0

Simplifying this equation, we get:

(x - 5)(y - 6)²(z - 5)² = 0

Now, we can substitute the values of x, y, and z with the given coordinates (6, 8, 7) and simplify further to find the equation of the tangent plane at that point.

Therefore, the equation of the tangent plane to the surface 2(x - 5)² (y - 6)² (z - 5)² = 10 at the point (6, 8, 7) is (x - 5)(y - 6)²(z - 5)² = 0.