math20c Meesue Yoo fall 09 quiz6

# math20c Meesue Yoo fall 09 quiz6 - Quiz 6 Solution for MATH...

This preview shows pages 1–2. Sign up to view the full content.

Quiz 6 Solution for MATH 20C, 2009 1 . Let f ( x,y ) = e x - xe y . (a) Find the critical points of the function f . Ans. f x = e x - e y = 0 e x = e y , or x = y, f y = - xe y = 0 x = 0 By solving two equations x = y and x = 0, we get x = 0 ,y = 0. So, the critical point is (0 , 0). (b) Use the Second Derivative Test to analyze the critical points. Ans. f xx = e x f xy = - e y f yy = - xe y D = - xe y · e x - ( - e y ) 2 = - xe x + y - e 2 y . At the critical point (0 , 0), D (0 , 0) = - 1 < 0 Hence, (0 , 0) is a saddle point. 2 . Find the volume of the largest rectangular box in the ﬁrst octant with three faces in the coordinate planes and one vertex in the plane x + 2 y + 3 z = 6. Let x , y and z be the three sides of the rectangular box. Then the volume of the box is f ( x,y,z ) = xyz. Deﬁne g ( x,y,z ) by the given constraint g ( x,y,z ) = x + 2 y + 3 z = 6 . We apply the Lagrange multiplier method and ﬁnd all x , y , z and λ values satisfying f = λ g, x + 2 y + 3 z = 6 . f

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

math20c Meesue Yoo fall 09 quiz6 - Quiz 6 Solution for MATH...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online