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If f (x,y) = In(x² + y²), then fx(x,y) + fyy(x, y) is: а. 0 x+y b. x2+y2 2х+2у с. x²+y2 d. Undefined

If f (x,y) = In(x² + y²), then fx(x,y) + fyy(x, y) is: а. 0 x+y b. x2+y2 2х+2у с. x²+y2 d. Undefined

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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If f (x,y) = In(x² + y²), then fxx(x,y) + fyy(x, y) is: а. 0 x+y b. x2+y2 2х+2у с. x²+y2 d. Undefined Suppose f (x, y) is differentiable, has only one critical point at (x, y) = (a, b) and has continuous second-order partial derivatives within a neighbourhood of that critical point. Which of the following is not necessarily true at (a, b)? a. That fxy(x, y) = fyx(x, y). b. That fx (x, у) %3 f, (х, у) 3D 0. c. That the sign of frx(x, y) is the same as that of fyy(x, y) if the Second Derivative Test is conclusive. d. That f(x, y) attains a relative extremum or has a saddle point if the Second Derivative Test is conclusive.
Transcribed Image Text:If f (x,y) = In(x² + y²), then fxx(x,y) + fyy(x, y) is: а. 0 x+y b. x2+y2 2х+2у с. x²+y2 d. Undefined Suppose f (x, y) is differentiable, has only one critical point at (x, y) = (a, b) and has continuous second-order partial derivatives within a neighbourhood of that critical point. Which of the following is not necessarily true at (a, b)? a. That fxy(x, y) = fyx(x, y). b. That fx (x, у) %3 f, (х, у) 3D 0. c. That the sign of frx(x, y) is the same as that of fyy(x, y) if the Second Derivative Test is conclusive. d. That f(x, y) attains a relative extremum or has a saddle point if the Second Derivative Test is conclusive.
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