Question

Find the equation of the tangent plane to the surface
4x−2y^2−3z^2=−5
at the point (x,y,z)=(4,3,1)
z =

Answer 1

Step 1 :

An equation of the tangent plane to the surface  at the point is

.

The equation is and the point is .

Rewrite the equation as z as function in terms of x and y.

Step 2 :

Let .

Apply partial derivative on each side with respect to x.

Substitute the point in above equation.

Step 3 :

The function is .

Apply partial derivative on each side with respect to y.

Substitute the point in above equation.

Step 4 :

At the point , the equation of a tangent plane to the surface is

.

Substitute and in above equation.

The equation of a tangent plane to the surface is .

Solution :

The equation of a tangent plane to the surface is .