Gilbert_Hmwk14sol - moseley (cmm3869) HW14 Gilbert (56380)...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: moseley (cmm3869) HW14 Gilbert (56380) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points In the contour map below identify the points P, Q , and R as local minima, local maxima, or neither. 3 2 1-1-2-3-2-1 1 2 Q P R A. local maximum at Q , B. local minimum at P , C. local minimum at R . 1. C only 2. A and C only 3. A and B only 4. all of them 5. A only 6. B and C only 7. B only correct 8. none of them Explanation: A. FALSE: the point Q lies on the 0- contour and this contour divides the region near Q into two regions. In one region the contours have values increasing to 0, while in the other the contours have values decreasing to 0. So the surface does not have a local minimum at Q . B. TRUE: the contours near P are closed curves enclosing P and the contours decrease in value as we approch P . So the surface has a local minimum at P . C. FALSE: the contours near R are closed curves enclosing R and the contours increase in value as we approch R . So the surface has a local maximum at R , not a local minimum. keywords: contour map, local extrema, True/False, 002 10.0 points Locate and classify all the local extrema of f ( x, y ) = x 3 y 3 + 3 xy 1 . 1. local min at (0 , 0), saddle point at (1 , 1) 2. local max at (1 , 1), local min at (0 , 0) 3. local min at (1 , 1), saddle point at (0 , 0) correct 4. local max at (1 , 1), saddle point at (0 , 0) 5. local max at (0 , 0), saddle point at (1 , 1) Explanation: Since f has derivatives everywhere, the crit- ical points occur at the solutions of f ( x, y ) = f x i + f y j = 0 . But f x = 0 when f x = 3 x 2 + 3 y = 0 , i.e., y = x 2 , moseley (cmm3869) HW14 Gilbert (56380) 2 while f y = 0 when f y = 3 y 2 + 3 x = 0 , i.e., x = y 2 ....
View Full Document

Page1 / 5

Gilbert_Hmwk14sol - moseley (cmm3869) HW14 Gilbert (56380)...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online