x WeBWorK England MAT x C Essential Calculus Early Tr X M Outlook.com alifbrashe

Question

x WeBWorK England MAT x C Essential Calculus Early Tr X M Outlook.com alifbrashec X Bb Blackboard Learn C https://webwork.asu.edu MAT 267 Spring 2015 Section 11.7/7/ /webwork2/England View equations as Images Correct Math Jax Show saved answers Yes At least one of the answers above is NOT correct. No Use Equation Editor? 1 pt) Find the absolute maximum and absolute minimum of the function f(z, y) zy 6y 36z 216 on the region on or above Yes y z2 and on or below y 39 No As usual, ignore unneeded answer blanks, and list points lexicographically. Apply options Absolute minimum value: 36 EEE and attained a 0 Absolute maximum value: 39 EEE and attained a (6 Note: You can earn partial credit on this problem. Preview Answers Submit Answers Your score was recorded You have attempted this problem 3 times. You received a score of 40% for this attempt. Your overall recorded score is 40%. You have unlimited attempts remaining. 11:44 PM 3/9/2015

Explanation / Answer

Solution:

f(x,y) = xy -6y -36x +216

Now,

f x = y-36         and f y = x-6

At <0,0>

y=36   and x=6

Therefore , we got only one critical point : (6,36)

(6,36) also lies on y=x^2 ans below y=39 . Hence acceptable.

Now,

f xx = 0 , f xy = 1 , f yy =0 , f yx =1

Hessian of f(x,y) =

| f xx    f xy |

| fyx     f yy |

=

| 0 1|

|1 0|

= -1

Since , Hessian of f(x,y) < 0 ,

( 6 , 36 ) is a saddle point .

Related Questions

Navigate

• Browse (All)
• Browse X
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.