Question

Find the point(s) on the surface at which the tangent plane is horizontal.

Answer 1

Step 1 :

The equation is .

Apply partial derivative on each side with respect to x.

Differentiate z  partially with respect to y.

Step 2 :

The slope of the horizontal tangent plane is zero.

Equate to zero.

Equate to zero.

Multiply equation (2) by 2 and add to the equation (1).

Substitute in equation (1).

Substitute and in z.

The tangent plane is horizontal at the point .

Solution :

The tangent plane is horizontal at the point .