Consider the function f(x, y) = 6y2 +4x2- 12xy- 4y. Then: O None of these O (1,-2/3) is a critical point and f has a saddle point at (-1,-2/3) O (1,1) is a critical point and f has a local maximum at (1,1) O (1,-2/3) is a critical point and f has a local minimum at (-1,-2/3)

Q: Which of the following is TRUE about the function g(x, y) = yt + T? (0, T) is a critical point of g.…

A: The given function is: g(x,y)=y4+π

Q: Find the values of x, y and z that correspond to the critical point of the function: z = f(x, y) =…

A:

Q: 18: Which of the following functions has no critical points? A: f(x) = -x² + x² B: C: f(x) = x³ + x2…

A: This is the question of multi-variable calculus.

Q: 4. Show that: f(x) = 2²²₁ x+1 f'(x) = = 4x (1+x²)(1+x)(1-x) (x¹+1)² a. What are the critical points…

A: Given functionL:- fx=2x2x4+1

Q: What is the critical point of the following function? f(x, y) = xy² (2 - x - y) Choose the correct…

A: The critical point of a function of two variables is a point at which both partialderivatives  and…

Q: Show that the function f(x, y) = 3x e² - 2³-e³y has exactly one critical point and that f has a…

A: Some important definitions:

Q: If (1,1) is a critical point of f(x,y) = x³ – 3x + 3y² – 6y then (1,1) is:

A: (1,1) is the local minimum point   explanation is given in below step

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.

Q: D

A:

Q: 2. Consider the function f(x, y) = x³ + 3x² – 3xy? + 6xy – 3y² + 6y + 98. (a) Find all critical…

A: Given fx,y=x3+3x2-3xy2+6xy-3y2+6y+98. Find fx, fy, fxx, fyy, fxy.…

Q: , Find and classify all critical points of the function f(z.y, z, w) = + +322 + u + 3ry + 6zz + 5zw…

A:

Q: If (1,1) is a critical point of f(x, y) = x³ – 3x + 3y2 - 6y then (1,1) is: O a local maximum a…

A: f(x,y)=x3-3x+3y2-6y  has  critical point (1,1)

Q: f(t) = V (2t - 1)

A:

Q: ht(s) of 1+x² f(x) = 1+x

A:

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

A:

Q: Which of the following are critical points of f(, y) = xy? – x + 8y+1. Select all that apply. (0, 0)…

A: First differentiate wrt x and y and then put equal zero

Q: The critical Points of f(x, y) - x' -3x +3y2-6y are: None of these O (1,1) and (-1,1). O (01) and…

A: We will find the first order partial derivatives of f and equate them to 0 to find the critical…

Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…