Answered: Find the local minimizers of: (a) f(x,…

Find the local minimizers of: (a) f(x, y, z) = x² + 3y² +z subject to x² + y² +z² = 16. (b) f(x, y, z) = x² + 2xy+3y² +4x + 5y + 6z subject to x+2y= 3 and 4x + 5z = 6.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.2: Applications Of Extrema

Problem 1YT: Find two nonnegative number x and y for which x+3y=30, such that x2y is maximized.

See similar textbooks

Related questions

Q: The union of two subspaces of a vector space is not necessarily a subspace.

Q: Solve for the variable using a method of your choice. An equation editor is not required for…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: A1. Consider the system of equations f(x, y, b) = x² bxy + y² - 1 = 0, g(x, y, b) = x² + y² + b² - 5…

A: The given system of equation is around the point .To find with that satisfies the equation.If is…

Q: 3. Consider the function f(x) = sin x. (i) Is there a sequence of polynomials converging uniformly…

Q: Let G be the set of all real-valued functions fon R such that f (x) cannot equal 0 for all x E R.…

Q: 1. Is the sequence bounded, monotone, and convergent or divergent? If it is convergent, find the…

Q: Let S = {[0, 1, −1, 2]T, [1, 2, 3, 0]T} ℃ R4 (a) Is S linearly independent? (b) If S is linearly…

Q: 5. v₁ = (1, 0, 0), V₂ = (0, -2, 0), V3 = (0, 0, 3)

A: The given vectors are as follows:To Find:whether the given vectors u and v are linearly dependent or…

Q: 1 Find the Taylor series of centered at z = -3. 2

Q: Find the area bounded by the given curves. r = 0 (0 ≥ 0), 0 = 0, 0 = 3

Q: ∞ 1 - sin(x) (x + 1)² : I = fº dx Please find the following from information below; 1) Use the p…

Q: 5. Consider the differential equation x'y" +8x²y" +9xy'-9y=0. Verify that the given solution…

A: The given differential equation is .To verify: The given solution functions form a fundamental set…

Q: (a) R4x7 (b) The real linear space (c) The space of all diagonal 6 x 6 matrices C² 2

A: Here, we have to find the dimensions of given linear spaces.

Q: Where does the subsequence series Nk = 2kpi come from? While I know it's used to specify the set of…

Q: Consider this system of equations: x1x2x3 = -10 2x1 + 3x2 + 5x3 = 46 x12x2 + 3x3 = 20 A. Write the…

Q: vectors >) Find a linearly independent set of vectors that spans the same subspace of Rª as that…

A: We have to find the linearly independent set of vector for the given set of vectors.

Q: Exercise 8.9.1 Find the algebraic and geometric multiplicity of each eigenvalue of the following…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find all values of x where the tangent line is horizontal for the function f (x) = x/x^2+5

Q: Consider (V x F)-ndS where F = 14e²²+y²i + 10e ²³ j + ln(z+ 13).xºs y k and S is the top half (2 ≥…

Q: 7. For all odd integers x and y, x² + 3y² = 0 (mod 8).

Q: St 1- order OPE, is there If y + x²y = sin(xy) analytical Solution for it ? If not, is numerical…

Q: 1. A particle moves along a straight line with velocity v(t) = t cos meters per second after t…

Q: Supposer FCE, acE is algebraic F and dog (a/F) 13 odd. Proveo that F(a)= F(a²). over

Q: Check the true statements below: A. A basis is a spanning set that is as large as possible. B. The…

Q: The rotation matrix R= rotate the vector v = O [1 2] O O O K2 27 [cos (0) -sin (0) sin (0) cos (8)…

A: The rotation matrix when multiplied to a vector counter clockwise by an angle .Given . The…

Q: Problem #9: Use the divergence theorem to find the total flux of flow field F out of the 6 sides of…

Q: Let U be a vector function of position in R3 with continuous second partial deriva- tives. We write…

A: In this mathematical exposition, we are tasked with demonstrating two important vector identities…

Q: D) y y(0) c) y" + 4y + 3y = 8(t-2), y(0) = 1, y'(0) = -1

Q: Find the maximum and/or minimum value(s) of the objective function on the feasible set S. (If an…

Q: Hello, can you help me solve problem? Thank you! Give a counterexmple: 1. Every convergent sequence…

Q: Let w, x, y, z be vectors and suppose z = 3x +y and w = −12x − 3y + 4z. Mark the statements below…

A: Let two set of vectors {u1,u2,⋯,un} and {v1,v2,⋯,vm} then Span(u1,u2,⋯,un)=Span(v1,v2,⋯,cm)iff every…

Q: A homeowner has a mortgage payment of $996.10, an annual property tax bill of $590, and an annual…

Q: 3. Use elementary row operations to write the augmented coefficient matrix in reduced row echelon…

A: Given that the system of equations is:

Q: be a vector space

Q: $25,000 is deposited for 5 years in an account earning 5% interest. (Round your answers to two…

Q: Let V and W be vector spaces over a field F. Prove that V is isomorphic to W if and only if dim(V) =…

A: Let V and W be vector spaces over a field F. We prove that V is isomorphic to W if and only if…

Q: Y(s) = - 2s e s² + 4s +3 Find the inverse Laplace transform of the following function

A: We have to find Laplace inverse of Y(S) =

Q: Discussion - Counting and Probability - Counting with Look-a-likes (MLO6.5) How many unique words…

A: Solution:- Count the total number of letters in the word "Tallahassee". There are 11 letters in the…

Q: Solve the equation (3+y+ xy) dx +(3+x+xy) dy = 0.

Q: In Exercises 9-12, which of the given subsets of C[1,1] are subspaces of C[-1, 1]? 9. F = {f(x) in…

Q: Please answer the following question attached below; Information; ∞ f(x) = Σman. n=0 Please find the…

Q: For any given positive integer m, find the Laurent series for 0 2. 1 zm (2-2) on the annulus

Q: 3x2y''+x(1+x)y'-y=0 What is the general solution of the differential equation using Forbenius…

Q: Find the wronskian for the set of functions. {e^*, xe−X, (x + 2)e X} X HER

Q: Write this function as a step function 1 0 3 f(t) =

A: The given problem is to express the given function as a step function.Given f(t) = 1 0≤t<1 ,…

Q: 5. Compute A63, where 4-621 A =

Q: Using the priority list T2, T3, T7, T6, T₁, T4, T5, schedule the project below with two processors.…

A: Given the digraph and the priority list as We will use list processing algorithm.1) On the digraph,…

Q: question 2

A: We have to find the volume.for this we using the formula

Q: angle of Two medians drawn from acute angles of a right angled triangles intersect at an pi/6. If…

A: Two medians drawn from acute angles of a right angled triangles intersect at an angle of . If the…

Q: f(x) = 1/x. Please find the following from information below; 1) Determine first four, non-zero…

Question

Find the local minimizers of:
(a) f(x, y, z) = x² + 3y² + z subject to x² + y² + z² = 16.
(b) f(x, y, z) = x² + 2xy +3y² + 4x + 5y +6z
subject to x + 2y = 3 and 4x + 5z = 6.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: We use to find local minimizer by Lagrange multiplier method.

VIEW

Step 2: Calculation to setup the given function in the Lagrange multiplier method.

VIEW

Step 3: Calculation to find the partial differentiation of the function.

VIEW

Step 4: Find the function value at the points (x,y,z).

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Use the Method of Lagrange Multipliers to find the largest product that the positive numbers x, y, and z can have if x+y+= = 16.
Minimize: z = 4x + 8y subject to: х+ 1.5у 2 45 2х + 0.5у > 40 х + у < 40 х, у 2 0
Maximize B=xy2, where x and y are positive numbers such that x+y2=10.
Use the Lagrange multiplier method to find the values of x and y that minimise the function 2x2 + y² subject to the constraint x + y = 1.
Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x²+y² + z² subject to the constraint xª + y4 + z4 = 1.
Find the best quadratic approximation, Q(x, y) of √9 - 7x + 4y for (x, y) 7x+4y near (0,0), Q(x, y): =
Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = xy subject to the constraint that 4x² + y² = 8.
Find the local minimizers of: (a) f(x, y, z) = x² + 3y² + z subject to x² + y² + z² (b) f(x, y, z) = x² + 2xy + 3y² + 4x + 5y + 6z subject to x + 2y = 3 and 4x + 5z 6. = = 16.
Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = xy²z³ (if they exist) subject to x2 + y2 + 2z² = 100.
Minimize Q=4x2+3y2, where x+y=7.
Find two nonnegative numbers x and y such that xy = 60 and 5x + 3y is minimized. y =
Use Lagrange multipliers to find the minimum and maximum values of f(x, y) = x + 3y, subject to the restriction that 2x² + 3y² = 14.