Question

Let f(x, y) = (2y-x^2)(y-2x^2) a. Show that f(x, y) has a stationary point at (0,...

Let f(x, y) = (2y-x^2)(y-2x^2) a. Show that f(x, y) has a stationary point at (0, 0) and calculate the discriminant at this point. b. Show that along any line through the origin, f(x, y) has a local minimum at (0, 0)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2. (i) Find the stationary...
Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2. (i) Find the stationary points of f. (ii) For each stationary point P found in (i), determine whether f has a local maximum, a local minimum, or a saddle point at P. Answer: (i) (0, −2), (2, 1), (−2, 1) (ii) (0, −2) loc. max, (± 2, 1) saddle points
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that...
(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x, y) ≥ 0 for all (x, y). Hint: find the minimum value of H. (4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin is a critical point for f which is a saddle point, even though on any line through the origin, f has a local minimum at (0, 0)
Let f(x,y) = 3x^2 + cos(Pi*y). a) f has a saddle point at (0,k) whenever k...
Let f(x,y) = 3x^2 + cos(Pi*y). a) f has a saddle point at (0,k) whenever k is an odd integer b) f has a saddle point at (0,k) whenever k is an even integer) c) f has a local maximum at (0,k) whenever k is an even integer d) f has a local minimum at (0,k) whenever k is an odd integer.
Calculate the following: absolute maximum, absolute minimum values of f(x, y) = 2x^2y on -> 2x^2+y^2=6
Calculate the following: absolute maximum, absolute minimum values of f(x, y) = 2x^2y on -> 2x^2+y^2=6
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and...
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) = (2y − z, x − z, y + 3x). Use matrices to find the composition S ◦ T. 2. Find an equation of the tangent plane to the graph of x 2 − y 2 − 3z 2 = 5 at (6, 2, 3). 3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...
Let f(x,y)=2ex+y. Find the second-order Taylor polynomial for f(x,y) at the point (0,0). Group of answer...
Let f(x,y)=2ex+y. Find the second-order Taylor polynomial for f(x,y) at the point (0,0). Group of answer choices 2+x+y+12x2+12y2 2x+2y+x2+y2 2+2x+2y+x2+2xy+y2 2−2x−2y+x2−xy+y2 None of the above.
Find the absolute maximum and absolute minimum values of f(x,y) = x^2 + 2y^2 − 2x...
Find the absolute maximum and absolute minimum values of f(x,y) = x^2 + 2y^2 − 2x + 2 on the closed disk D: x^2 + y^2 ≤ 4. Answer: absolute min: f(1, 0) = 1; absolute max: f(−1, ± √3) = 11
Let f(x, y) = −x 3 + y 2 . Show that (0, 0) is a...
Let f(x, y) = −x 3 + y 2 . Show that (0, 0) is a saddle point. Note that you cannot use the second derivative test for this function. Hint: Find the curve of intersection of the graph of f with the xz-plane.
1. Let f(x, y) = 2x + xy^2 , x, y ∈ R. (a) Find the...
1. Let f(x, y) = 2x + xy^2 , x, y ∈ R. (a) Find the directional derivative Duf of f at the point (1, 2) in the direction of the vector →v = 3→i + 4→j . (b) Find the maximum directional derivative of f and a unit vector corresponding to the maximum directional derivative at the point (1, 2). (c) Find the minimum directional derivative and a unit vector in the direction of maximal decrease at the point...
(9) (a)Find the double integral of the function f (x, y) = x + 2y over...
(9) (a)Find the double integral of the function f (x, y) = x + 2y over the region in the plane bounded by the lines x = 0, y = x, and y = 3 − 2x. (b)Find the maximum and minimum values of 2x − 6y + 5 subject to the constraint x^2 + 3(y^2) = 1. (c)Consider the function f(x,y) = x^2 + xy. Find the directional derivative of f at the point (−1, 3) in the direction...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT