1. f(x) = Vx2 – 4 (x²–9) 2. f(x) х+3 х+8 3. f(x) x2 +x-2

Q: One of the critical points of f(x,y) = x³ – 5y² + 10y – 27x is:

A: The given function is fx,y=x3-5y2+10y-27x. The critical points of a function f(x, y) are obtained by…

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

A:

Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

A:

Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

A:

Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

A:

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

A:

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: 37. f(x,y) = 9-x² – 7y³; f.(3, 1), fy(3, 1)

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

A:

Q: 11. f(x) = x² + 7x + 10 Opens up/down: Vertex: Axis of symmetry: Solution(s): y-int:

A:

Q: 4. Determine all the critical points for the function f(t) = Vt² (2t + 1)

A:

Q: Find the general solution of F′(x) = 1/x2, x > 0 and find the particular solution that satisfies…

A:

Q: 3.fCx)3D63X²4X+2 x<1 2x-1 X71 Part A: IS f(X) lontinuous ar X-1? JustfY answer. Palt…

A:

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: x+2 32 dt at x = 4. 2+t 6 Find the linearization of f(x) = 3-

A:

Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

A:

Q: The derivative of y= (V x - 2 )(Vx+1) is equal to: х - 1 A 2x+1/x-2 2х-1 B Jx+1/x=2 2х-2 2/x+1/x-2 D…

A:

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

A:

Q: of of and ду Find f(x,y) = Vx + 3y?

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: 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: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

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: What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have…

A:

Q: 4. F(x) = (1- t) dt %3D 4

A:

Q: The function f(z) 2x-36z+120z-8 has two critical numbers. The smaller one is x = and the larger one…

A: A critical point is a point in the domain of the function where the function is either not…

Q: The antiderivative of the function 4 .3 + 10x³ is, 4 f(x) - -4 .3 + 2.5x³ + c 4 -10 + 1.0xª + c -4 +…

A: According to question given f(x)=44.3+10x3We have to calculate the antiderivative

Q: 9. f(x.y. z) = In(x + 2y² + 322); P(-1, 2.4): u = -i- j - k

A:

Q: -5z Calculate F" (2) if F (x) = |(1- t)dt. %3D +1 O F' (2) = 5 (1– 252?) O F' (x) = 1- 24a? %3D O F…

A: We will use the formula Where

Q: The antiderivative of the function 4 + 10x is. x2 f(æ) = 4 + 5.0x2 + c - -4 5.0x2 + c -10 + 2.0x2 +…

A:

Q: Find f(x) by solving the initial-value problem. f'(x) = 3e*- 10x; f(0) = 5 %3D f(x) %3D

A:

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: what is the antiderivative F(x) 0f f(x)=3x^((1)/(2))-x-1that satisfies the condition F(4)=0 A,…

A: Given that:f(x)=3x1/2-x-1, F(4)=0

Q: ∇⋅F of F = (2x3y)i-(3y2z)j+(xz3)k at (1,2,-1). a. 27 b. -34 c. 4 d. -7

A: The del operator is used to represent the partial derivatives with respect to the variables defined…

Q: Show that the linearization of f(x) = (1 + x)k at x = 0 is L(x) = 1+ kx.

A: We need a linear approximation formula for f(x).

Q: Solve the following optimization problem by using Lagrange method: Maximize f(x,x;)=2x, + x, – 3x²…

A: Lagrange Multiplier Method:- This method is used to optimize a function on a region that contained…

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: Find X1 & X2 using Newton's method to minimize x2 – y2/2 starting from (1,1)

A:

Q: 3 9 dx dt -1 -3 with x(0) 4 Give your solution in real form. X1 = X2 = ||

A:

Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

A:

Q: In(|(2 +1)"(z + 3)|l) 15x - 13 dx = X (Don't forget to include the constant of 2-2x 3…

A: topic - indefinite integral

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: Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5

A: (64-x2)dydx=1⇒dy=dx64-x2integrating,                ∫dy=∫dx64-x2+c      [c=…

Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

Q: 1. f(x) = Vx - 1 at x = 5 %3D 2. f (x) = at x = 2 x-2

A:

Q: 3 The antiderivative of the function f(x) = + 9x is x2 -3 4.5x2 + c 3 + 18.0a? + c 6- + 1.5x + c 3 +…

A:

Q: If Newton's method is used to find the critical number of f(x) = a® – a³ + æ² – 2x with initial…

A: Image is attached with detailed solution.