The function f (x, y) = 3x3+y2-9x+4y is given. a) Find the critical points of function f. b)Do these functions have the local maximum, local minimum and saddle points at these points? Determine

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Q: 1. Given that f ( x , y ) = xy² - y? - 2x? + 10 , find the critical points and determine the…

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Q: Consider the function f(x) = 0.5 (x,² – x,)² + 0.5(1 – x,)² where x = [x1 x2]' . a. Determine the…

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Q: Find the local maximum minimum values and saddle point(s) of the function S(x, y) = 9 – 2x + 4y – x²…

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Q: 8. Determine if the critical point (0,0) of f(x,y) =x³+2xy² – y4 +x² + 3xy+y² +10 is a local…

A: f(x,y) = x3 + 2xy2 - y4 + x2 + 3xy + y2 + 10 => fx = 3x2 + 2y2 + 2x + 3y      fxx = 6x + 2…

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Q: 6. Find all critical points of f(x,y) = 2yt + x2 – 6xy and classify each critical point as a local…

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Q: Find and classify all critical points of f(x, y) = x3 +y3 -x² -y? + 20y + 10. (Order your answers…

A: we find all critical point offx,y=13x3+13y3-12x2-92y2+20y+10

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Q: The function f (x, y) = x³y + y3 – 3x?y + 2 has critical points at (0,0), (2,), (2, -) and (3,0).…

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Q: Consider the function f(x, y) = 2x³y² − 9x²y² + 12xy² + y Compute the stationary points of the…

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Q: Consider (x, y, z) = x² + y² + z² + 2xyz. Show that (0,0,0) and (-1, 1, 1) are both critical points.…

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Q: Let f(x, y) = x* + y* – 4xy. (a) Find all critical points of f. (b) For each critical point of f,…

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Q: 6. Find all critical points of f(x, y) = 2y4 + x2 – 6xy and classify each critical point as a local…

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Q: Find the critical points of f(x,y) = x³ + y³ + 3xy + 5, and classify them. (That is, at each…

A: Given f(x,y)=x3+y3+3xy+5 To find critical points: fx=0  and fy=0  will give critical points…

Q: Show that the function z = f(x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given a function in two variablesz=fx,y=x3-3x2-4y2+2

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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: 3. Find all critical points of the functionsf (x,y) = e2y (x2 + y?) and determine whether the…

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

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Q: Consider (r, y, z) = x² + y? + 2? + 2ryz. Show that (0,0,0) and (-1, 1, 1) are both critical points.…

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Q: Use the second derivative test to identify any critical points and determine whether each critical…

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Q: Use the second derivative test to identify any critical points and determine whether each critical…

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

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Q: 16 Let f(x, y) = x² + +y² 16 -. Classify all critical points of this function as being local…

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