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MAT 211- Lecture 5

by: Brigette Maggio

MAT 211- Lecture 5 MAT 211

Marketplace > Arizona State University > Math > MAT 211 > MAT 211 Lecture 5
Brigette Maggio
GPA 3.9

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These notes cover MAT 211- Lecture 5 on Sections 15.2 and 15.3.
Math for Business Analysis
Dr. Mohacsy
Class Notes
Math, MAT 211
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This 2 page Class Notes was uploaded by Brigette Maggio on Friday January 29, 2016. The Class Notes belongs to MAT 211 at Arizona State University taught by Dr. Mohacsy in Fall 2015. Since its upload, it has received 28 views. For similar materials see Math for Business Analysis in Math at Arizona State University.


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Date Created: 01/29/16
MAT 211­ Lecture 5­ Review 15.2 & 15.3  Review Section 15.2    Homework #14:  gt= 5x­0.46 gt (10,3)= 5(3)­ 0.4(10)= 11  gx= 5t­2x gx (10,3)= 5(10)­ 2(3)= 44  1.) When you study t=10 hours and GPA x=3.0, 1 additional hour of study would increase  the exam’s score by 11 points.  2.) An additional 1 point on GPA would increase the exam’s score by 44 points.    gt (10,3)/ gx (10,3)= 11/44= ¼    gt (10,3) =¼ gx (10,3)  ­Additional hour of study would increase your exam’s score by 11.  ­Additional GPA point would increase your exam’s score by 44.  ­Additional ¼ GPA point would increase your exam’s score by 11.    Homework #15:  A (P,r,t)= Pe^rt (80, 0.2, 8)  a.) AP= e^rt= 4.95       Ar= tPe^rt= 3169.94       At= rPe^rt= 79.25    Section 15.3­ Maxima and Minima    1​ ­Critical points where f​ = 0  ­Critical points were candidates for relative extrema.  ­To find critical points, set equal to zero.    ­Saddle point at (a,b)    ­Ex.: f(x,y)= 4x​+3y​ +6 Locate and classify the critical points.  where fx=0 fx=8x= 0 x=0  where fy=0  fy=6y= 0 y=0  (0,0)= critical point ­­­­­> candidate for min., max., or saddle point    fxx= 8 fxx (0,0)=8  fyy=6 fyy (0,0)=6  fxy=0 fxy (0,0)=0    H (0,0)= fxx (0,0) * fyy (0,0) ­ [fxy (0,0)] ^2    8             * 6           ­ 0^2 = 48Relative min. at (0,0)    If H is positive:   ­Relative min. if fxx (a,b) > 0  ­Relative max. if fxx (a,b) < 0  If H is negative:  ­Saddle point at (a,b)  If H = 0:  ­test is inconclusive    Homework #6:  g(x,y)= 1­3​2­x­2y​+y Locate and classify critical points.    1.) gx = ­6x­1= 0 x= ­⅙  gy= ­4y+1= 0 y=­¼          2.) gxx= ­6 gxx (­⅙, ¼)= ­6  gyy= ­4 gyy (­⅙, ¼)= ­4  gxy= 0 gxy (­⅙, ¼)= 0    H (0,0)= ­6 * ­4 ­ 0^2= 24 > 0  Because fxx (a,b) < 0 or gxx= ­6 <0, it is a relative (­⅙ , ¼)   


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