quiz2sol

# quiz2sol - MATH 203 FALL 2009 TAKE HOME QUIZ#2 SOLUTION...

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

MATH 203, FALL 2009, TAKE HOME QUIZ # 2: SOLUTION This is a closed book quiz, take 20 minutes. Due Monday 10/19/09. Question 1: Let f ( x, y ) be a map from R 2 R , and x = g ( s, t ), y = h ( s, t ) for some functions g, h : R 2 R . Assume f, g, h have derivatives of all orders. Let k ( s, t ) = f ( g ( s, t ) , h ( s, t )). Using the chain rule, calculate 2 k ∂s∂t . Solution: ∂s∂t k ( s, t ) = ∂s∂t f ( g ( s, t ) , h ( s, t )) = ∂s ( ∂f ∂x ∂g ∂t + ∂f ∂y ∂h ∂t ) (by the chain rule) = ∂s ( ∂f ∂x ) ∂g ∂t + ∂f ∂x ∂s ( ∂g ∂t ) + ∂s ( ∂f ∂y ) ∂h ∂t + ∂f ∂y ∂s ( ∂h ∂t ) (product rule) =( 2 f ∂x 2 ∂g ∂s + 2 f ∂y∂x ∂h ∂s ) ∂g ∂t + ∂f ∂x 2 g ∂s∂t + ( 2 f ∂x∂y ∂g ∂s + 2 f ∂y 2 ∂h ∂s ) ∂h ∂t + ∂f ∂y 2 h ∂s∂t (chain rule) = f xx g s g t + f xy h s g t + f x g ts + f yx g s h t + f yy h s h t + f y h ts (different notation) 1

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

View Full Document
2 MATH 203, FALL 2009, TAKE HOME QUIZ #2: SOLUTION Question 2: Find the critical point(s) of f ( x, y ) = x 2 + y 2 + 16 /x - 1 /y and classify them using the second derivative test.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern