3. Consider the following functions: f(z)) = x² + 16 9(=)) = (x – 16)² h((x)) = (x + 1)² – 16 Determine the difference between the solutions of f(x), g(x), and h(x).

Q: (b) Solve for the optimum to the following problem using the Karush-Kuhn Tucker conditions: Optimise…

A: Solve the following using the Karush-Kuhn Tucker conditions: Optimise fx1,x2=x1x2s.t.…

Q: Find a solution of by fixed point method for f(x)=x^3+x-1=0 ?

A:

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: Given function f(x)=mx+b where m and b is constant our aim To evaluate linearization of f(x) at…

Q: 1. A company manufactures and sells a televisions per month. If the cost and the revenue functions…

A:

Q: 2. Find and classify the critical points of the function f (x, y) = 6x2 – 2x³ + 3y? + 6xy

A: The solution is given below in the next step:

Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 3x2 – 4x + 8 has a tangent…

A:

Q: 21) Find the maximum and/or minimum values of f (x, y) = x² + 2xy + 2y² - 6y + 2

A:

Q: If f(x) = x – kx-1 has a relative maximum at x = -2, then the value of k is %3D

A:

Q: +] has the general solution u(x, y) = e"[f(x)+g(y)] where f and g g are arbitrary functions

A: ∂2U∂xdy+∂u∂x=0let U(H.Y)=e-yf(x)+g(y)

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx +b at any given…

A: Givenf(x)=mx +b where m and b are constantsTo find linearization of f.

Q: 28. Find the critical points of f(x) = x3 – 3x2 - 3. а. (0,—3)аnd (2, -7) b. (0,3)and( 2,7) c. (0,2…

A:

Q: x'y" – 3xy' +4y=x° Inx

A:

Q: particular

A: We find particular solution.

Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 4x2 – 8x + 4 has a tangent…

A:

Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

A:

Q: Зх +1 5. Determine the critical point/s of the function f(x) %3D V3x2 + 2

A:

Q: 2. Identify the iterative function f(x) = x3 – 9x2 – 6 if initial approximation x, = 2.25

A:

Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

A:

Q: If f(x)=1/5x^5 - 3/4x^4 - 4/3x^3 +60, then what is the set of c value for which f has a relative…

A:

Q: Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

A:

Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x) =…

A:

Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: x² +y F(x,y)=- x- y - is a homogeneous function of degree

A: Topic= Function Degree =1

Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

A:

Q: der the problem maxx + 2y subject to x² + y² ≤ 1 and x + y 20

A:

Q: 9. Let f(x) = x³ – 3x² + 3. a. Find the y-intercept of the function; b. Find all critical points of…

A:

Q: Verify that y = h(x) =- (C is an arbitrary constant, x # 0) is a solution of xy' = -y.

A:

Q: Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x² + 3y + 3x + 3xy +1.

A: First calculate the partial derivatives, gx, gy  for g(x,y) . Solve the equations, gx=0 , gy=0…

Q: Suppose that x-y" + axy' + by = 0 has the general solution of the following form: y = C,x³ + C2x³ In…

A:

Q: 1. Find the relative maxima and minima of y by the second-derivative test: (a) y = --2x? + 8x + 25…

A: Consider the provided question, According to you we have to solve the part (b), (c) and (d). (b)

Q: Find the particular solution determined by the initial condition. P(X) = 2x ° = 3x )= -6 2/5 - 3x:…

A: This belong to initial value problem of differential equation.first we solve the differential…

Q: Find and classify all critical points of each of the function: a.f (x, y) = (x² +x + 1)e¬²/10-y² f…

A: Solution is given below:

Q: 1. Eliminate the arbitrary constants in the equation given by: (x- a)(y – b) = 1 |

A:

Q: Use the IVT to show that e−x2 = x has a solution on (0, 1).

A: Given equation is

Q: 12. If f(x) is a non-constant linear fucntion and g(x) is a quadratic function, then what type of…

A: f(x) is linear function so f(x) can be expressed as  f(x)=ax+b, where a≠0 and b are constants. g(x)…

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: The given function is: f(x)=mx+bSo,f'(x)=m

Q: x² + y² F(x, y) =- - is a homogeneous function of degree

A: For finding degree of homogeneous function, Put x=hx and y=hy

Q: Show solution/process. 1. f(x) = 2x² – 4x + 5 at the point (–1,11) 2. f(x) = v25 – x² at the point…

A: Since there are more than one question, only one question can be answered. The function is given by,…

Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

A:

Q: Find the critical points of the function f(x)=x2−4x+3x−2.

A:

Q: Find minimum and maximum for the function 6 x + 4 y under conditions: x2 0; yz 0; -x+y s 12; x+ys…

A: The objective is to find maximum and minimum value of the function 6x+4y.

Q: Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) = (x…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 1. Determine the nature of the stable points of the function f (x, y) = x²y – x² – 3xy + 3x + 2y –…

A:

Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: 1 Find the general solution of x'y" +xy' -y= x+1

A:

Q: Find the critical point of the function f(x, y) - 4+ 7x – 5x² + 6y + 7y?

A: