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)

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

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
Question : y''+6y'+9y=0,y(0)=2,y'(0)=1 , 4y''+12y'+9y=0,y(0)=2,y'(0)=2 y''-y'-2y=cosx , y''+3y'+2y=x^2 - e^2x , y''-3y'+2y=sinx  , y''-2y'-3y=3e^2x
Question : y''+6y'+9y=0,y(0)=2,y'(0)=1 , 4y''+12y'+9y=0,y(0)=2,y'(0)=2 y''-y'-2y=cosx , y''+3y'+2y=x^2 - e^2x , y''-3y'+2y=sinx  , y''-2y'-3y=3e^2x
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT