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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find the points on the cone z2 = x2 + y2 that are closest to the point (4, 2, 0).

To determine

To find: The points on the cone z2=x2+y2 which is closest to (4,2,0)

Explanation

The given cone equation is, z2=x2+y2 .

The distance d between (4,2,0) and any point (x,y,z) is,

d=(x4)2+(y2)2+(z0)2d2=(x4)2+(y2)2+z2

Substitute the value of z2 in the above equation.

d2=(x4)2+(y2)2+x2+y2

Thus, f(x,y)=(x4)2+(y2)2+x2+y2 .

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

fx=x((x4)2+(y2)2+x2+y2)=x(x4)2+x(y2)2+x(x2)+x(y2)=2(x4)(1)+0+2x+0=4x8

Hence, fx=4x8

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Chapter 14 Solutions

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