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8. In this problem we'll find the points on the curve y = 1.5 – 2² that are closest to the origin. (a) Here is a graph of the curve y = 1.5 – 2². Visually estimate the coordinates of the points where the curve is nearest the origin. 0.5 -2.5 -2 -1.5 -1 -0.5 0.5 1.5 2 2,5 -0.5 -1 (b) Let f(x, y) = x² + y² represent the square of the distance from (0, 0) to a point (x, y). Use the method of Lagrange multipliers to minimize f subject to the constraint y = 1.5 – x². Hint: what is g(x, y) in this problem?

8. In this problem we'll find the points on the curve y = 1.5 – 2² that are closest to the origin. (a) Here is a graph of the curve y = 1.5 – 2². Visually estimate the coordinates of the points where the curve is nearest the origin. 0.5 -2.5 -2 -1.5 -1 -0.5 0.5 1.5 2 2,5 -0.5 -1 (b) Let f(x, y) = x² + y² represent the square of the distance from (0, 0) to a point (x, y). Use the method of Lagrange multipliers to minimize f subject to the constraint y = 1.5 – x². Hint: what is g(x, y) in this problem?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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8. In this problem we'll find the points on the curve y = 1.5 – a² that are closest to the origin. (a) Here is a graph of the curve y = 1.5 – 2². Visually estimate the coordinates of the points where the curve is nearest the origin. 15 0.5 -2.5 -2 -1.5/ -0.5 0.5 1 1.5 2.5 -0.5 -1 (b) Let f(x, y) = x² + y² represent the square of the distance from (0, 0) to a point (x, y). Use the method of Lagrange multipliers to minimize f subject to the constraint y = 1.5 – x². Hint: what is g(r, y) in this problem? (c) If D represents the minimum distance from the curve to the origin, sketch the circle f(x, y) = D² on the graph. What do you notice about the points you solved for above? (d) Calculate Vf at the points you found above, and sketch the vector Vf at each point. What is the relationship between Vf and the circle f(x, y) = D²? 2.
Transcribed Image Text:8. In this problem we'll find the points on the curve y = 1.5 – a² that are closest to the origin. (a) Here is a graph of the curve y = 1.5 – 2². Visually estimate the coordinates of the points where the curve is nearest the origin. 15 0.5 -2.5 -2 -1.5/ -0.5 0.5 1 1.5 2.5 -0.5 -1 (b) Let f(x, y) = x² + y² represent the square of the distance from (0, 0) to a point (x, y). Use the method of Lagrange multipliers to minimize f subject to the constraint y = 1.5 – x². Hint: what is g(r, y) in this problem? (c) If D represents the minimum distance from the curve to the origin, sketch the circle f(x, y) = D² on the graph. What do you notice about the points you solved for above? (d) Calculate Vf at the points you found above, and sketch the vector Vf at each point. What is the relationship between Vf and the circle f(x, y) = D²? 2.
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