Find the directional derivative of the function in the direction of u = cos(8)i + sin(8)j. fx, y) = 7 8= - 7x + y'

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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Find the directional derivative of the function in the direction of u = cos(8)i + sin(8)j.
flx, y) = 8 -
7x + у
Transcribed Image Text:Find the directional derivative of the function in the direction of u = cos(8)i + sin(8)j. flx, y) = 8 - 7x + у
(x, y) = 9x2 + 4y?
c = 85, P(3, -1)
(a) Find the gradient of the function at P.
Vr(3, -1) =
(b) Find a unit vector that is normal to the level curve (x, y) = c at P.
(c) Find the tangent line to the level curve (x, y) = c at P.
(d) Sketch the level curve, the unit normal vector, and the tangent line in the xy-plane.
-6
-4
-2
4
4
하
2
-과
Transcribed Image Text:(x, y) = 9x2 + 4y? c = 85, P(3, -1) (a) Find the gradient of the function at P. Vr(3, -1) = (b) Find a unit vector that is normal to the level curve (x, y) = c at P. (c) Find the tangent line to the level curve (x, y) = c at P. (d) Sketch the level curve, the unit normal vector, and the tangent line in the xy-plane. -6 -4 -2 4 4 하 2 -과
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