Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

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Q: Find the maximum value of ƒ(x, y) = x²y6 for x, y ≥ 0 on the unit circle. fmax =

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Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: Show that the function y = x1/2, x > 0, is strictly concave

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Show that the maximum value of f (x, y) = x 2 y3 on the unit circle is

A: We should maximize f(x,y)=x2y3 under the constraint gx,y=x2+y2 where x2+y2=1. Now, ∇f=2xy3,…

Q: Calculate the maximum and minimum of the function f (x,y) = xy subject to the condition x2 + y2 = 1

A: To find the optimal solution, we will use Lagrange multiplier method. The Lagrangian function is…

Q: II Find the maximum value M of f(x, y) = x4y5 for x ≥ 0, y ≥ 0 on the line x + y = 3. (Use symbolic…

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Q: ind the absolute maximum and minimum values of f(x,y) = {(x, y) : y ≥ x², y ≤ 4}. = 3x² + 2y² - 4y…

A: Solution :  To find the absolute maximum and minimum values of f(x, y) = 3x ^ 2 + 2y ^ 2 - 4y on the…

Q: Let f (x, y) = A− (x2 + bx + y2 + Cy). What values ​​of A, B, C give f a local maximum value of 15…

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Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Find the point P where the function f(x, y, z) = x¹y¹z7 reaches the maximum value for x, y, z ≥ 0 on…

A: Given the function fx,y,z=x4y4z7 reaches the maximum value for x,y,z≥0 on the unit sphere x2+y2+z2=1

Q: Show that V₂ = C1 CiYt-i+1 is stationary

A: As per the question we are given a stationary process {Yt} having the acf (auto-correlation…