James Stewart

ISBN: 9781305266643

Textbook Problem

The plane 4x – 3y + 8z = 5 intersects the cone z² = x² + y² in an ellipse.

(a) Graph the cone and the plane, and observe the elliptical intersection.

(b) Use Lagrange multipliers to find the highest and lowest points on the ellipse.

To determine

To sketch: The graph of the cone z2=x2+y2 and the plane 4x−3y+8z=5 and observe the elliptical intersection

The cone equation is, z2=x2+y2 .

The plane equation is, 4x−3y+8z=5 .

Calculation:

Consider the equations, z2=x2+y2 and 4x−3y+8z=5

To determine

To find: The highest and lowest on the ellipse by using Lagrange multipliers.

Check out a sample textbook solution.

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The plane 4x – 3y + 8z = 5 intersects the cone z2 = x2 + y2 in an ellipse. (a) Graph the cone and the plane, and observe the elliptical intersection. (b) Use Lagrange multipliers to find the highest and lowest points on the ellipse.

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Math
Calculus Multivariable Calculus 8th Edition

The plane 4x – 3y + 8z = 5 intersects the cone z² = x² + y² in an ellipse.

(a) Graph the cone and the plane, and observe the elliptical intersection.

(b) Use Lagrange multipliers to find the highest and lowest points on the ellipse.