5. These are the level curves of a smoothly varying function f(x, y) 4 (a) At P is fx positive or negative? Why? (b) At P is fxx positive or negative? Why? (c) Sketch Vf at P and Q on the level curve f(x, y) = 3. 5. These are the level curves of a smoothly varying function f(x, y) 4 (a) At P is fx positive or negative? Why? (b) At P is fxx positive or negative? Why? (c)...
f 2. Figure 10 shows a constraint 9 (x, y) = 0 and the level curves of a function f. In each case, determine whether has a local minimum, a local maximum, or neither at the labeled point. 4 3 2 Vf Vf 4 3 2 А B g(x, y) = 0 g(x, y) = 0 Rogawski et al., Multivariable Calculus, 4e, © 2019 W. H. Freeman and Company FIGURE 10
The graphs show the constraint and several level curves of the objective function. Use the graph to approximate the indicated extrema. (a) Maximize z = xy; Constraint: 2x + y = 4 .C =2 c 4 = 6 (b) Minimize z =x2 + y2; Constraint: x + y - 4 = 0 Need Help? Talk to a Tutor The graphs show the constraint and several level curves of the objective function. Use the graph to approximate the indicated extrema. (a)...
2. For f(x.y)-9-9x2-y'* a. Sketch the surface z-f(x,y) b. Sketch at least 3 level curves (label each one with its function value) 2. For f(x.y)-9-9x2-y'* a. Sketch the surface z-f(x,y) b. Sketch at least 3 level curves (label each one with its function value)
Please complete #3. 2. Let f(x,y,z 3x2 + 4y2 +5z2- xy - xz - 2zy +2x -3y +5z. Apply 20 steps of Euler's method with a step size of h 0.1 to the system x'(t) y(t)Vf(x(t), y(t), z(t)) z'(t) (x(0), y(0), z(0)) = (-0.505-08) to approximate a point where the minimum of f occurs. Give the value of x (2) (which is the x coordinate of the approximate point where the minimum occurs). Note: This process is called the modified...
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 2...
final study guide, please help 1.) Sketch the indicated level curves of the following functions. 0, z = 2, and z = 4 level curves of f(x,y)-хуз. The z =-2, z ). log025 (x + y2 2 level curves of h(x,y) -1,2-0, z-, 1, and z ii. The z ii. The z7, z 4,z 3, z 2, and z1 level curves of g(x.y) +3 1.) Sketch the indicated level curves of the following functions. 0, z = 2, and z...
Question 7 (8 points) Let vf(x,y) denote the gradient field for the function f(x, y) = x2 - y. Sketch a level curve and two gradient field vectors on the level curve.
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
2. (4 pts) Let f(x,y) =x2+y2. Mark the locations where f attains its minimum and maximum on the triangle constraint shown in Figure 1. Clearly indicate “minimum” or “maximum” at each location. 2 0 X FIGURE 1. Figure for Problem 2. 2. (4 pts) Let f(x, y) = x2 + y². Mark the locations where f attains its minimum and maximum on the triangle constraint shown in Figure 1. Clearly indicate "minimum" or "maximum" at each location.