9. Let f(x, y) = 3x* +2y² +50 . There is a critical point at А) (10, 4) В) (5, 2) C) (-10, -4) D) (0, 0) E) (1, 1)

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A: fx, y=3x2y+y3-3x2-3y2+2 We have to find all critical points of the given function.

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Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

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Q: 1. Consider the paraboloid f(x,y) = ax² + bry + cy², where we will assume that a, c# 0. We will…

A: As per the guidelines of Bartleby for more than one question asked, only two is to be answered, you…

Q: 2 4 2) f(x,y)=2xy- 5x? - 2y² +4x+4y – 4 Ans. f 3'3 0 local max. %3D

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Q: . Let f(x, y) = x3³-3x+3xy2. Then f has critical points (0, -1), (0, 1), (-1,0), and (1,0). Use the…

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Q: 13. If (1,3) is the critical point for f(x) = x² + ax + b, then b = A) 4. B) 5. C) -2. D) 2.

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Q: Let W (s, t) = F(u(s, t), v(s, t)) where W,(1,0) = = Wt(1,0) = u(1,0) = 5, u, (1, 0) = 5, ut(1, 0) =…

A: Let where To find .

Q: 10. Find and classify all the critical points of f (x, y) = x² + y¹ — 4xy + 1 g(x, y) = x² + xy + y²…

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Q: 1. R= {(1, 1), (2, 2), (3, 4), (5,9)} C ZX Z 2. R= {(n, m) ENXZ: n² = m} CNXZ 3. R = {(n, m)…

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Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: 3. If F(x, y) = 3x¹y³ – 2x²y³, find F(x, y)/y²

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Q: 522 – 7z+3 dz - 12 dt 15w – 13u? + w dw f) e) d)

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Q: Minimize f(x,y,z) = x² + y² + z² subject to - 2x + 6y + 4z = − 56. X=

A: I have explained everything with in the solution. Please go through that.

Q: x-y x+y+1' 1. Let f(x, y) (a) f(2, 1) (b) f(1,2) (c) f(a, a) (d) f(y + 1,y) Find:

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Q: 8. The function f(x, y) = x² + 4y² - 8x + 16y - 2 has one critical point. Determine its location and…

A: We have to find critical point and its location Topic:- Application of derivative.

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A: f(x) = ax3 + bx2 + cx + d  Point of inflection is (0,4)  So, f(0)   =   4  i.e.    a(0) + b(0) +…

Q: 10. Suppose the joint PMF of (X, Y) is given by (0, 1), (1,0), (2, 1) otherwise (a) Are X and Y…

A: f(x,y)=1/3; you (0,1),(1,0),(2,1) Result:  X and Y are independent iff p(X=x,Y=y)=P(X=x)P(Y=y)…

Q: 12. Find and classify all critical points for (Баллов: 2) f (x, y) = 3x²y + y – 3x² – 3y² + 2 %3D O…

A: Let's find.

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A: We are asked to which is true for the given condition  Note: Critical points are points where the…

Q: 7. Find and classify all critical points of the function f(z, y, z, w) = a +y? + 3:2 + w? + 3ry +6rz…

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Q: Suppose we know the following: z = f(x, y) where x = 2v-u, y=v² +2u, (-3,2)= 12, fy(-3,2)= -15,…

A: Given: z=fx,y where x=2v-u, y=v2+2u The partial derivatives fx-3,2=12, fy-3,2=-15, fx-1,-2=-8,…