\ \

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 .