What is g'(x) when g(x) = In (x³ + 3x2 + 5x + 6)? Select the correct answer below: 1 23+3x2+5x+6 3x2+6x+5 In (x3+3x2+5a+6) O In (3a2 + 6x + 5) 23 +3x? +5x+6 3x2 +6x+5 3x2+6x+5 x3+3x2+5x+6

Q: Find the critical number for y = f(x) = x (x + 2)²

A: NOTE: Refresh your page if you can't see any equations. . the given function is take derivative…

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: 7. Find all the critical points of f(x) = (x² – 4x – 4) e² %3D and classify them.

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Q: f f(x) = ln(x2+10x+16) ov

A: The absolute minimum of f(x) is 6ln(2) and the absolute maximum of f(x) is 4ln(2)

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

A: The given function is

Q: Determine the critical point/s of f(x) = ln(x² + 4x + 14) on [-4,2]. 0x= -3 Ox=1 0 x = 0. 0x = -2

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Q: Find the values of a and b such that f(x) = x³ + ax² + bx + 5 has x = 1 and x = 2 as critical…

A: The function f(x)=x3+ax2+bx+5 has critical points at x=1 and x=2

Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

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Q: Show that (0, 0) is a critical point of ƒ(x, y) = x2 + kxy + y2 no matter what value the constant k…

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Q: Find the critical numbers of f(x) = ln(x2 + 5x + 14).

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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…

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Q: Find ther critical point x* of 2 f(x)=312921 22 −5+1 73 +7x₂² +372 73 +6x3² − 3x₁ +3x₂ + 3xg +8…

A: As per the question we are given a quadratic multivariate function f(x) And a constraint g(x) = -8…

Q: 1. Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) =…

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Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: 7  please answer, type the solution if you can please. or write clearly

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Q: The function f(x) = 2x – 45x + 300x – 5 has two critical numbers. The smaller one is x : %3D and the…

A:

Q: Suppose we have a function z = a > 0. f(x, y) = -x² – y² + a(x +y) where a is exogenous and a.…

A: The given equation is z=fx,y=−x2−y2+ax+y Where a is exogenous and a > 0.

Q: 2.) Find the critical values for g(x) = x²e-2x

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Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: 1. Find all critical points and investigate the type and stability of each. x' = xy - 2 y' = x - 2y

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Q: Let f(x)=(7+3x)4   f(x) has one critical value at A =

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Q: The function f(x) = 2x° 39x + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Topic = Derivative

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

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Q: 11. If f(r) = rª and g(r) = r³, then f' (x) = 4x³ and gʻ(x) = 3x². The Chain Rule multiplies…

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Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

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Q: 1. f(x) = 3x + 4, at x = 4 2. f(x) = 3x2 – x + 2 at x = 2 3. f(x) = ***, at x = 1 x+3 4. f(x) = X-1…

A: As per guidelines we can solve only three subparts at a time, so the first  three subparts can be…

Q: Determine the GINI Index of Country X whose Lorenz curve is f(x) =;x² +÷x*. If Country Z 3 has a…

A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

Q: 1. f(x) = x² – 4x + 1 at point (0,1) 2. f(x) = x³ + 2 at point (1,3) 3. f(x) = 2x* + 3x³ – 2x + 7 at…

A: Given : The functions and the points.

Q: ,2 Let f(x) = x – 12x -27x + 1. Find the critical points of f(x).

A: Find the derivative as follows: f'x=ddxx3-12x2-27x+1        =3x2-24x-27

Q: 98x2.1for one year to y

A:

Q: 8. Use the fact that the critical points of f(x, y) are found when vf(x,y) = 0 to show that (-3,-2)…

A:

Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: have critical points at x=2 and x--2 f(x) = x² + 4x + 4

A: Critical points:x=2 , x=-2

Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A: Given: Lorenz curve for first year: y = 0.97x2.1 And for the next year: y = 0.35x2 + 0.65.

Q: 4 If the critical number of the function f(x) =x is x 0, then the function %D is decreasing on (0,0)

A: We can find the decreasing interval as below.

Q: Find all the critical points of the function f(x) = x^3 - 2x^2 - 15x + 2 on the interval [-1, 3]

A: Let's find.

Q: Find the critical points and the intervals on which the function f(x) = (x³ – 4x) e* + 15 is…

A: given f(x)=x3-3247xex +15 we have to find the critical points and the intervals on which the given…

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: 6 Find the critical numbers of the function f(x) = x5 - * – 12x2 .

A: The given function is  fx=x65-12x12.

Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

A:

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: 2. Evaluate f(x) = e3x + 2 at x = -1. Round to the nearest thousandth. %3D %3D f(-1) = ...

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Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

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

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Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.

A: Given function is,