   Chapter 14, Problem 7RCC

Chapter
Section
Textbook Problem

How do you find a tangent plane to each of the following types of surfaces?(a) A graph of a function of two variables, z = f(x, y)(b) A level surface of a function of three variables7 F(x, y, z) = k

(a)

To determine

To find: The tangent plane of the function z=f(x,y) .

Explanation

Use the following steps given below to find the tangent plane of the function z=f(x,y) .

Step 1:

Consider the function z=f(x,y) .

Let the tangent at the point be (a,b,c) .

Find partial derivative with respective x in the function z=f(x,y) at the point (a,b,c) .

fx|(a,b,c)=fx(a,b,c)

Find partial derivative with respective y

(b)

To determine

To find: The tangent plane of the surface F(x,y,z)=k .

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