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Let f(x, y) = x4 + y4 - 2x2 + 4xy - 2y2 has a minimum at (-√α, √α) and (√α, - √α) Find the value of α.
Correct answer is '2'. Can you explain this answer?
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Verified Answer
Let f(x, y) = x4 + y4 - 2x2 + 4xy - 2y2has a minimum at (-√&alph...
⇒
Solving, we get 
r = 12x2 - 4
s = 4
t = 12y2 – 4
at (-√2, √2)
r = 20, s = 4, t = 20
rt - s2 > 0 and r > 0 ∴ minimum
s = 4
t = 12y2 – 4
at (-√2, √2)
r = 20, s = 4, t = 20
rt - s2 > 0 and r > 0 ∴ minimum
The correct answer is: 2
Most Upvoted Answer
Let f(x, y) = x4 + y4 - 2x2 + 4xy - 2y2has a minimum at (-√&alph...
Unfortunately, the given function does not have a minimum at a specific point. The function f(x, y) = x^4 + y^4 - 2x^2 - 4xy - 2y^2 is an equation of a surface in 3-dimensional space. It does not have a minimum or maximum at a single point. Instead, it may have local minimum or maximum points or saddle points on the surface. To find these points, you would need to find the critical points by taking partial derivatives with respect to x and y and setting them equal to zero. Then, you can use the second partial derivative test to determine whether these critical points are local minimum, maximum, or saddle points.
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Let f(x, y) = x4 + y4 - 2x2 + 4xy - 2y2has a minimum at (-√α,√α) and(√α, - √α)Find the value ofα.Correct answer is '2'. Can you explain this answer?
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