6. Let f(x, y) = x³ – 2y² – 2yª +3x²y. Find all the points (x, y) where Vf(x,y) = Ō = (0, 0). Such points are called critical points. Here is one way to do this. Find all points (x, y) that satisfy both equations fr(x, y) = 0 and fy(x, y) = 0. fa = 0: 3x2 + 6xy = 0, fy = 0: - 4y – 8y³ + 3x2 = 0. Start with fr = 0. Solving this gives two cases, Case I (x = 0) and Case II (y = -x/2). I: Case I is x = 0. Apply x = 0 to the second equation, fy point. 0, to find one critical II: Case II is y = -x/2. Apply y = -x/2 to the second equation, fy = 0, to find three critical points. Make a list of critical points by combining what you found in Case I and Case II. If you find a point (a, b) twice, only list it once

Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

A:

Q: F(x, y,z)= (4xyz) î + (-2xz+2yz) ĵ -3y² z k , find VxF

A:

Q: Please don't provide handwritten solution ...

A:

Q: Find the functions x*(r) and y*(r) such that x = x*(r) and y = y*(r) solve the problem max f(x, y,…

A: max fx , y, r=max-x2-xy-2y2+2rx+2ry To Find: x*r , y*r such that x=x*r ,y= y*r.

Q: 3. Show that f(x, y, z) fxx + fyy+fzz = 0. = 1 x² + y² + z² satisfies the equation

A:

Q: Let r = x² + y – z and z³ – xy + yz + y³ = 1. Assume that x and y are independent ar is variables.…

A: Introduction :

Q: Write the Linear Approximation to f(x, y) = x(1 + y)−¹ at (a, b) = (8, 1) in the form f(a+h,b+k)≈…

A:

Q: h(x, y) = cos(7x + 13y) Find k such that h(x, y) = k has no solutions. Show that h(x, y) = 1 is a…

A:

Q: For the function f(x,y) = 6 of find and 8x+3y' dx dy

A:

Q: Find all values of x and y such that f(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 4xy…

A: To find all values of  such that  simutaneously.