Compute the gradient of the function at the given point. f(x, y) = 5x2 + 10y, (4,-3) Vf = 80i - 30j %3D O Vf = 40i + 10j Vf = 160i - 30j %3D Vf = 40i - 30j

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 58E
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Please answer both questions they are urgently needed
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Question 1
Compute the gradient of the function at the given point.
f(x, y) = 5x2 + 10y, (4,-3)
Vf = 80i - 30j
Vf = 40i + 10j
Vf = 160i - 30j
Vf = 40i - 30j
Moving to another question will save this response.
Transcribed Image Text:A Moving to another question will save this response. Question 1 Compute the gradient of the function at the given point. f(x, y) = 5x2 + 10y, (4,-3) Vf = 80i - 30j Vf = 40i + 10j Vf = 160i - 30j Vf = 40i - 30j Moving to another question will save this response.
A Moving to another question will save this response.
Question 2
Find all the local maxima, local minima, and saddle points of the function.
f(x, y) = x² - 6x + y2 - 16y - 6
O f(-3, 8) = -43, saddle point
O f(3, 8) = -79, local minimum
O f(3, -8) = 177, saddle point
f(-3, -8) = 213, local maximum
A Moving to another question will save this response.
MacBook A
Transcribed Image Text:A Moving to another question will save this response. Question 2 Find all the local maxima, local minima, and saddle points of the function. f(x, y) = x² - 6x + y2 - 16y - 6 O f(-3, 8) = -43, saddle point O f(3, 8) = -79, local minimum O f(3, -8) = 177, saddle point f(-3, -8) = 213, local maximum A Moving to another question will save this response. MacBook A
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