1) The region of integration of I is represented by the blue region in: O a Oc. Od 2) By reversing the order of integration of I, we get: a 1 = $secx dxdy b. I = 8 secx dxdy c. 1 = secx dxdy d. 1 - IL secx dxdy Exercise 6. Double Integral in rectangular coordinates (10 pts 10 pts) Let I= secx dydx. 1) The region of integration of I is represented by the blue region in:...
Exercise 5. Extreme values (8 pts+12 pts) Let f(x, y) = 2x2 - 4x + y2 – 4y +1. 1) The number of critical points of f is: a. 0 b. 1 c. 2 d. 3 2) The point (1,2) is: a. a local maximum for f b. a local minimum forf c. a saddle point for f
Exercise 5. Extreme values (8 pts+12 pts) Let f(x,y) = 2x2 - 4x + y2 – 4y +1. 1) The number of critical points of f is: a. 0 b. 1 c. 2 d. 3 mi b. d. 2) The point (1,2) is: a. a local maximum for f b. a local minimum for f c. a saddle point forf b. C.
Exercise 5. Extreme values (8 pts+12 pts) Let f(x,y) = 2x2 - 4x + y2 – 4y +1. 2) The point (1,2) is: a. a local maximum for f b. a local minimum for f c. a saddle point for f O a. b. O c.
Suppose f(x,y)=xy(1−10x−4y)f(x,y)=xy(1−10x−4y). f(x,y)f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, determine whether the critical point a local maximum, a local minimim, or a saddle point. First point (____________,__________) Classification: Second point(__________,__________) Classification: Third point (___________,_________) Classification: Fourth point (__________,_________) Classification:
please show work, im so lost on all of these Given f(x, y) = 4x 5xys + 3y?, find f(x,y) = fy(x, y) = f(x, y) = 5x2 + 4y? $2(5, - 1) = Given f(x, y) = 4x2 + xy 4x² + xys – 67%, find the following numerical values: $:(3, 2) = fy(3, 2) = Given f(x, y) = 3x4 – 6xy2 – 2y3, find = fry(x, y) = Find the critical point of the function f(x, y)...
QUESTION 16 The function f(x,y) = x -x- y2 + 2y has O A. 1 local max. 1 local min. OB. 1 saddle pt. and 1 local min. O C2 local min. OD. 1 saddle pt. and 1 local max. O E 2 saddle pt.
QUESTION 23 The function f(x,y) = x3 – x- y2 + 2y has O A 1 saddle pt. and 1 local min. OB. 1 local max. 1 local min. OC. 2 saddle pt. OD. 1 saddle pt. and 1 local max. O E. 2 local min.
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
Problem 8. (1 point) For the function f(x,y) = 4x² + 6xy + 2y”, find and classify all critical points. O A. (0,0), Saddle O B. (4,6), Saddle O C. (4,6), Relative Minimum OD. (0,0), Relative Minimum OE. (0,0), Saddle |(4,6), Relative Maximum