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
39. Let L be the minimum length of a ladder that can reach over a fence of height h to a wall located a distance b behind the wall. a. Use Lagrange multipliers to show that L = (h2/3 + 62/3;3/2 (Eigure 20). Hint: Show that the problem amounts to minimizing f (x, y) = (x + b)² + (y+h)? subject to y/b = h/x or ry = bh. b. Show that the value of L is also equal to...
31. Let Q be the point on an ellipse closest to a given point P outside the ellipse. It was known to the Greek mathematician Apollonius (third century BCE) that PQ is perpendicular to the tangent to the ellipse at Q (Figure 16). Explain in words why this conclusion is a consequence of the method of Lagrange multipliers. Hint: The circles centered at P are level curves of the function to be minimized. Rogawski et al., Multivariable Calculus, 4e, ©...
Please describe the contour map and list important aspects of it, thanks! Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x, y) for which f(x, y) is a potential function, b) c) sketch a contour map of f (x, y) and, on the same figure, sketch F(x,y) (on R2). Comment on any important aspects of your sketch. Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x,...
QUESTION 26 AND 31 PLEASE SHOW STEPS THANK YOU SO MUCH J-2 J-V4-z² Ji 26. Let be the region below the paraboloid x2 + y? = z – 2 %3D that lies above the part of the plane * + Y + z = I in the first octant. Express f (x, y, z) dV as an iterated integral (for an arbitrary function J). 27. Assume J (ª, Y, 2) can be expressed as a product, f (x, y, z)...
Given F(x, y) = (x²y3, xy). (a) Determine if F is conservative. If yes, find the scalar potential. (b) Evaluate F.dr where is the path defined parametrically by r(t) = (13 – 2t, t3 + 2t) e/F c for 0 < t < 1.
Minimize f(x,y) = x2 + xy + y2 subject to y = - 6 without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x,y). Use the constraint to rewrite f(x,y) = x² + xy + y2 as a function of one variable, g(x). g(x)=
Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the constraint glx.v) = -6x + 3y - 12. Find the optimal point of f(x,y) subject to the constraint g(x.). Enter the values of, y. f(x,y), and below. NOTE: Enter correct to 2 decimal places y f(x,y) A-
7) Given f(x,y)= x^2+y^2+2, subject to the constraint g(x,y)=x^2+xy+y^2-4=0, write the system of equations which must be solved to optimize f using Lagrange Multipliers.
f(x, y) = (xy explain while constraint is x xº+y4 = 16 this function can't have a maximum valde subject to the constraint explain why this function has to have a minimum vulve subject to the constraint