5.1 (10 points): Let f(x,y) = 4 – 22 – y? Find all extrema (both relative...
[1] (10 points) Find the relative extrema and saddle points for the function f(x,y) = x+y? - 6xy +8y. 121 (10 points) Use Lagrange multipliers to find the maximum value of the function f(x,y)=4-x? -y on the parabola 2y = x² +2.
Find all points where the function has any relative extrema or saddle points and identify the type of relative extremum. f(x,y) = x3 – 12xy + 8y3 A. Relative minimum at (2,1) and relative maximum at (0,0) OB. Relative minimum at (2,1) and saddle point at (0,0) OC. Saddle point at (2,1) D. Relative maximum at (1,2)
Find all points where the function has any relative extrema or saddle points and identify the type of relative extremum. f(x,y)= e-(x2 + y2 -by) A. Relative maximum at (0,3) OB. Saddle point at (0,3) O C. Relative maximum at at (0,3) and relative minimum at at (0, -3) OD. No relative extremum or saddle points.
19. Find the critical points, relative extrema, and saddle points of the function. a. f(x, y) = x2 + y2 +2x – 6y + 6 b. f(x, y) + y2 c. f(x, y) = x2 – 3xy - y2 = x²
2. Let f(x,)-21 be subjoct to the constraint z+y'4. (a) Find all candidate points for the locations of the absolute extrema lying inside the region given by+y4 Co,l) y -l Using the method of Lagrange multipliers, find all candidate points for absolute extreme along the boundary of the region given by+y4. (b) (c) Using your answers above, what are the absolute maximum and absolute minimum values of f over the given region? Clearly label and circle the absolute extrema (give...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
+ 1) Find all relative extrema for y = _ 13 x3 + 3x + 4 2) Find all absolute extrema of f(x) = 2x3 - 9x2 + 12x over the closed interval [ -3,3). Given: f(x) = 2x3 – 3x2 – 36x + 17 3) Find all critical values for f(x). 4) Find all relative extrema of f(x). 5) Find all points of inflection of f(x).
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...
1) find the relative extrema of the function f(x) = x^2+1/x^2 2) find relative extrema of the function and classify each as a maximum or minumum: f(x) = x^3-12x-4
In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4 g 12.) Use the method of Lagrange multipliers to minimize f(x, y) = x² + y² subject to the constraint equation - 3x + g = 30 (You do NOT have to verify that it is a minimum.