f(x, y) = x2 + y2 + 2xy + 6.
1- Find all the local extremas and 2) does the function f have an absolute max or min on R2
Cal 4 , ) and use this to 6. Let f(x,y) = x2 + y2 + 2x + y. (a) Find all critical points of f in the disk {(x,y) : x2 + y2 < 4). Use the second derivative test to determine if these points correspond to a local maximum, local minimum, or saddle point. (b) Use Lagrange multipliers to find the absolute maximum/minimum values of f(x, y) on the circle a2 +y -4, as well as the points...
consider the function f(x,y)=x^2-2xy+3y^2-8y (a)find the critical points of f and classify each critical point as local max min or saddle point (b) does f have a global max ?if so what is it ? does f have a global min ? if so what is it ?
QUESTION 2 Calculate and simplify det if f(x,y) = O x2 - y2 + 2xy (x2 + y2)2 O 4x(+- x² + 3y2) (x² + y²)3 o 4x(x² – 3y?) (x² + y²)3 OO O x2 - y2 + 2xy (x² + y²)?
Show that if x and y are real numbers, x2 + y2 >= 2xy and (x + y)2 >= 4xy; When does equality hold (with proof)? Show that if x and y are real numbers, x2 + y2 2xy and (x y) 2Hry. When does equality hold (with proof)?
Find the P.S. of the IVP: x2 + 2xy + y2 1+ (x + y)2 y(x = 0) = 4 Primes denote derivatives WRT X. (y'a
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.
Use Lagrange multipliers to find the min and max of f(x,y,z) = x2-y2+ 2z subject to the constraint x2 + y2 + z2 = 1.
Find the absolute min/max of on the domain f(,y) = x2 + y2 +r+y + 4 We were unable to transcribe this image
Find the absolute maximum and minimum of the function f(x, y) -ry1 on the domain D (r, y),y 20, x2 +y2< 1) rty+1 Find the absolute maximum and minimum of the function f(x, y) -ry1 on the domain D (r, y),y 20, x2 +y2
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...