Find the critical point of the function f(x, y) = 9x 3y- - In(\r+ y|). c = || Use the Second Derivative Test to determine whether it is OA. a local maximum OB. test fails C. a saddle point D. a local minimum

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A: The given function is y=cos θ+sin θ

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A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

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A: Second derivative test : Suppose (a,b) is a critical point of f. Assume fxx,fyy,fxy are defined and…

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Q: Find the critical points of the function f(r, y) = 8y+ local maxima or saddle points. - 24.ry and…

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Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

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Q: Find the critical point of the function f(x,y)=6x−2y^2−ln(|x+y|). c= Use the Second Derivative Test…

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A: Given function: Interval [1,6] For critical points, differentiate the function of y with respect to…

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A: To find- critical point and do the second derivative test.

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A: Given  ƒ(x) = x3

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Q: For what values of the constant k does the Second Derivative Test guarantee that ƒ(x, y) = x2 + kxy…

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Q: Find the critical point of the function f(x,y)=3e^x−2xe^y. c= Use the Second Derivative Test to…

A: f(x,y)=3ex-2xey First we find critical point from equations fx=0 and fy=0 Then,  Second Derivative…

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Q: On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between…

A: From the given graph of f'(x) to answer the given questions.

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A: Given function: For critical points:

Q: ) Use the second derivative test to classify each critical point of f (x,y)=-x' +4xy- 2y² +1 as a…

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Q: Find the critical point of the function f(x, y) = 24x – 4y² – In(|x + y|). - - c = Use the Second…

A: see below the answer and explanation

Q: For the function f(x,y)=x^2+2y^2−(x^2)y, does the critical point (−2,1) correspond to a local…

A: Given,  Critical Point: (-2, 1)

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Q: Find the minimum and maximum values of y = V120 - V6 sec e on the interval [0, ] fmin fmax

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Q: Find the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x >0, y>0)…

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Q: Find the critical point of the function f(x, y) = – (25x + 5y² + In(]x + y[). c = Use the Second…

A: As two questions are given, I will solve only one. Given , f(x,y)=-25x+5y2+lnx+y…

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Q: f (x, y) = xª – 4.x³ + 2x² + 8xy + 1.

A: To find out the critical points and classify them as relative maximum, minimum or saddle point.