Find the local minimizers of: (a) f(x, y, z) = x² + 3y² + z subject to x² + y² + z² = 16.

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) constraint that 4x² + y²…

A: In the given problem we have to find the maximum and  minimum value of a function subject to a…

Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

Q: Maximize B=xy2​, where x and y are positive numbers such that x+y2=10.

A:

Q: Find the maximal value of the function f(x,y)=2x3-y3 on the circle of equation x2+y2=7.

A: We have to find the maximal value of the function  on the circle of equation

Q: Find the best quadratic approximation, Q(x, y) of √9 - 7x + 4y for (x, y) 7x+4y near (0,0), Q(x, y):…

A: Step 1:Step 2:Step 3:Step 4:

Q: Minimize: =4x+5y Subject to: 10x 5y100 20x+10y 150 x+y12 0 y 20

A:

Q: Let f(x, y) = x² + y² - 4 2 y-2 Find fay(x, y).

A:

Q: Suppose that x and y are two positive real numbers so that x + y = 10. Maximize the product xy

A: To find the solution of the given problem use the second derivative test. Second derivative test:…

Q: Use the simplex method to minimize the function z=n*x1-x2-2x3 subject to the constraints in the…

A:

Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: Determine the convexity/concavity property of the following: (i) f(x1, x2) = 3xx2 + x – 3xỉ – 3x +…

A: In the given question we have to determine the convexity and concavity of the function…

Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: Use the Lagrange multiplier method to find the values of and y that minimise the function 2x2 + y²…

A: Let us consider the function f(x,y)  To determine the maximum and minimum value of the function…

Q: Find the point(s) on the line y = 7x + 3 closest to the point (−1, 8).

A:

Q: Consider the scalar IVP X= ✗ t+a x(o)=xo a>o Prove a unique solution exists for t>-a using a vector…

A: The detailed solution is provided below.Explanation:

Q: Find the point (x,y) on the line y=x that is equidistant from the points (3,8) and (−10,−10)

A: To find the point x, y on the line y=x, that is equidistant from the points 3, 8 and -10, -10.