Exercise 5. Extreme values (8 pts+12 pts) Let f(x,y) = 2x2 - 4x + y2 –...
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. 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.
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 Оа. Ob. Ос. Od 2) The point (1,2) is: a. a local maximum forf b. a local minimum forf a saddle point for c. Оа. Ob Oc. Let1 = f'secx dydx. .) The region of integration of I is represented by the blue region in b O a Od 2) By reversing...
1. Let f(x,y) = kx2 + y2 - 4xy. Determine the values of k (if any) for which the critical point at (0, ) is: (a) A saddle point (b) A local maximum (c) A local minimum
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)...
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...
(2 points) Find the maximum and minimum values of the function f(x, y) = 2x2 + 3y2 – 4x – 5 on the domain x2 + y2 < 100. The maximum value of f(x, y) is: List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). The minimum value of f(x,y) is: List points where the function...
Let f(x, y) = x(x – 1) + y2. (a) [1 point] Sketch the level curves of f. (b) [2 points] Compute the gradient of f, and sketch it as a vector field. (c) [3 points) Find all critical values of f and classify them as local maxima, local minima, or saddle points.
5. [-13 Points) DETAILS TANAPCALC10 8.R.029. Consider the following. Ax,y) - 2x2 + y2 - 12x - 4y + 4 Find the critical points of the function. (If an answer does not exist, enter DNE.) (x, y) = Use the second derivative test to classify the nature of each of these points, if possible. O relative maximum relative minimum saddle point inconclusive no critical point Finally, determine the relative extrema of the function. (If an answer does not exist, enter...
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