MATH-1326-THQ 7, 2016-02-29 11:39 (Printed First Name) (Printed Last Name) XXX0000 Net ID (First Letter of Last Name) 001 - 503 Section Take Home Quiz 7 Penalty Instructions 1. Fill in the requested information on the line above. 2. This handout is due at the beginning of lecture on Tuesday (03-08-2016). One point penalty per minute late. Submit right away, don't wait for the end of class! THQ with missing name will receive 10 points penalty. 3. This handout must be printed out and. You may print it single sided or double sided. Failing to print costs 10 points. 4. This handout must be stapled. Failing to staple costs 10 points. 5. Your work must be hand written on this handout. 6. You must show all work. You may receive zero or reduced points for insu cient work. 7. Your work must be neatly organized and written. You may receive zero or reduced points for sloppy work. 8. Only a subset of these questions will be graded. You will not be told which questions will be graded in advance. Due Date: Tuesday, 03-08-2016 Page 2 of 7 MATH-1326-THQ 7, 2016-02-29 11:39 Problem 1 Find all rst and second order partial derivatives for the following function. (i.e. Find fx (x, y), fy (x, y), fxx (x, y), fyy (x, y), fyx (x, y) and fxy (x, y).) (a) z = f (x, y) = x3 y 2 + x2 + y 4 + e(2x+y 2) (b) z = f (x, y) = x2 + x2 y 3 2y 3 + ln (x2 + 4y) Page 3 of 7 Problem 2 (a) Find the total dierential of p z = f (x, y) = f (x, y) = x2 + y 2 and compute it's value when (x, y) = (3, 4) and (dx, dy) = (0.02, 0.01). (b) Find the total dierential of f (x, y) = x + 3y 2x 3y and compute it's value when (x, y) = (1, 2) and (dx, dy) = ( 0.02, 0.01). (c) Find the total dierential of f (x, y) = ln 2x + y + 2 and compute it's value when (x, y) = (0, 0) and (dx, dy) = (0.3, 0.2). MATH-1326-THQ 7, 2016-02-29 11:39 Page 4 of 7 Problem 3 (a) Using the total dierentials, approximate p (12.001)2 + (4.998)2 (b) Using the total dierentials, approximate p 3 (1.001)2 + (1.01)3 + 6 MATH-1326-THQ 7, 2016-02-29 11:39 Page 5 of 7 MATH-1326-THQ 7, 2016-02-29 11:39 Problem 4 Find all critical points for following functions. Classify each critical point as a relative minimum, relative maximum or saddle points. (a) f (x, y) = 4xy 4x2 10y 2 8x 8y 8x + 6y 7 (b) f (x, y) = x2 + y 2 xy 10 Page 6 of 7 MATH-1326-THQ 7, 2016-02-29 11:39 Problem 5 Find all critical points for the function f (x, y) = x3 27x y 3 + 6y 2 + 7 Classify each critical point as a relative minimum, relative maximum or saddle points. Page 7 of 7 MATH-1326-THQ 7, 2016-02-29 11:39 Problem 6 Find all critical points for the function f (x, y) = x + 25 16 +y+ +5 x y Classify each critical point as a relative minimum, relative maximum or saddle points