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9. Find the point on the curve y x² closest to the point (0, 1).

9. Find the point on the curve y x² closest to the point (0, 1).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The lecture is about optimization . This is calculus 1
9. Find the point on the curve y = x² closest to the point (0, 1). 10. Find the point on the curve y = x² closest to the point (3, 4). 11. Find the point on the curve y = cos x closest to the point (0, 0). 12. Find the point on the curve y= cos x closest to the point (1, 1). 13. In exercises 9 and 10, find the slope of the line through the given point and the closest point on the given curve. Show that in each case, this line is perpendicular to the tangent line to the curve at the given point.
Transcribed Image Text:9. Find the point on the curve y = x² closest to the point (0, 1). 10. Find the point on the curve y = x² closest to the point (3, 4). 11. Find the point on the curve y = cos x closest to the point (0, 0). 12. Find the point on the curve y= cos x closest to the point (1, 1). 13. In exercises 9 and 10, find the slope of the line through the given point and the closest point on the given curve. Show that in each case, this line is perpendicular to the tangent line to the curve at the given point.
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