   Chapter 14.7, Problem 44E

Chapter
Section
Textbook Problem

Find the points on the surface y2 = 9 + xz that are closest to the origin.

To determine

To find: The points on the surface y2=9+xz which is closest to the origin.

Explanation

Given:

The surface equation is, y2=9+xz .

Calculation:

The distance d between (0,0,0) and any point (x,y,z) is,

d=(x0)2+(y0)2+(z0)2d2=x2+y2+z2

Substitute the value y2=9+xz in the above distance equation.

Thus, d2=x2+9+xz+z2

Let, f(x,y)=x2+9+xz+z2 .

Take the partial derivative of f(x,y) with respect x and obtain fx .

fx=x(x2+9+xz+z2)=x(x2)+x(9)+x(xz)+x(z2)=2x+0+z(1)+0=2x+z

Hence, fx=2x+z (1)

Take the partial derivative of f(x,y) with respect z and obtain fz

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Other Equations Find all real solutions of the equation. 96. 3+x=x2+1

Precalculus: Mathematics for Calculus (Standalone Book)

What is 834 of \$12,000?

Elementary Technical Mathematics

For

Study Guide for Stewart's Multivariable Calculus, 8th 