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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
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

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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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