Let f(x) = x* + 2x³ + 3x + 4 € Z3[x]. Then x = -1 is a root for f(x) of %3D multiplicity: None 4

Q: The function f(x) = 11 – 7x has an absolute maximum value of and this occurs at x equals

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Q: What is the value of a such that the function y = 2x4 - ax² + 3 has twin global minima at x = -3 05…

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Q: The total-revenue and total-cost funtions for producing x clocks are R(x)=500x-0.01x2 and…

A: The total-revenue and total-cost functions for producing x clocks are The profit function is

Q: Find the linear approximation to f(x)=x2+1x−2 near a=3.

A: Given: f(x) = x2 +1x − 2; a = 3

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given that,

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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Q: Find the particular solution determined by the initial condition. f'(x) = 3x2/3 - 4x3; f(1) = - 8…

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Q: Suppose that f(æ, y) = e-3x² – 4y? + y Then the maximum is

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Q: If we use the secant method on f(x) = x+x3+3 with X-2 0 and Xn-1 = 1, then Xn is_

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Q: Find the Critical Numbers of the Function: f(x) (x2 + 6x - 7)2

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Q: The function f(x) = 2x³ 30x? + 54x 6 has two critical numbers. The smaller one is x = and the larger…

A: We have to find

Q: Find the critical numbers of the function. a. f(x) = x³ + 6x2 – 15x

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Q: Show that a cubic function f (x) = x3 + ax2 + bx + c is increasing on (−∞,∞) if b > a2/3.

A: Given function is: fx=x3+ax2+bx+c Then we get, f'x=3x2+2ax+b

Q: b- Determine the critical point of the function f(x) = x5 – 5x* + 5x³ –- 1 %3D

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Q: Q No. 2 Discuss the differentiability of ƒ(x) = (x – 3)' at x = 3 by using definition and…

A: the given function is: f(x)=x-323 we have to discuss the differentiability of the given function at…

Q: 2. Calculate the point(s) of intersection of f(x) = 2x² + 4x – 11 and g(x) = -3x + 4.

A: Given f(x) = 2x2 + 4x - 11 and g(x) = -3x + 4

Q: find the interverse of the fuction f (x)= 2x + 3/x-4

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Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

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

A: We have to find value of k.

Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: 9. If f(x) = kx – 1 and f'(15) = 2, find k. %3D -

A: Given f(x)= kx3 - 1 and f-1(15)=2 then we have to find out the value of k

Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: Given: ƒ(x) = (4 + 3x)1/3

Q: Let f(x) = 2x² – 8x + 2. (a) Find the critical point c of ƒ and compute f(c). (Give your answers as…

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Q: Find the critical numbers of the function  f(x) = x3 + 6x2  - 15x

A: Solution -  Given function is given as- f(x) = x3+6x2-15x…

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

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Q: The domain of the function f(x,y) = In(2 – /x2 + y² ) is: %3D - x² +y² < 4

A: The explanation of the solution as follows:

Q: find the linearization of f(x)=x^2+4x-4 at x=2

A: Linearization formula, L(x)= f(a)+f'(a)(x-a)

Q: Find the positive critical point of the function f (x) %3D x4 + 7 x =

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Q: show steps please.

A: We will find the first two derivatives of F(x) We use the fundamental theorem of calculus To find…

Q: The function f(x) =x -x² – 2x – 1 is increasing over: %3D

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Q: . The function f(x, y)= 8x' - /4x* + 3y* is homogenous in x and y of degree -. The function f(x, y)=…

A: Here we have to find the degree of homogeneous function

Q: Find the linearzation L(x) of f(x)= \sqrt(5x+16) at a=0

A: Given Fx=5x+16 at a=0The objective is to find the linearzatin Lx ofFx=5x+16 at a=0find the…

Q: Find the particular solution determined by the initial condition. f'(x) = 3x273 - 6x; f(1) = - 7…

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Q: Find the maximum value of 5x2 - 4xy+ 8y subject to x+y? = 1..

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Q: The function f(x) = 4 – 7x* has an absolute maximum value of and this occurs at x equals

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Q: Determine the values of x at the critical points of f(x)=x -3x -0.25x+3.75 and classify each…

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Q: The function f(x) = 2x³ – 27x² + 48x 1 has two critical numbers. - The smaller one is x = and the…

A: We have to find the critical points for the function f(x)=2x3-27x2+48x-1.

Q: Find the local extremum  f(x)=x3+3x2-9x+6

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Q: Find the critical numbers of the function.   f(x)  = x3 + 6x2 -15x

A: Critical numbers of a function are the values of x for which its first derivative is zero or…

Q: Find the linearization L(x) of f (x)=- Vx -5 at a =3. – 5 2.

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Q: For what value of k will x + k/x have a relative maximum at x = -2?

A: Given: f(x)=x+kx

Q: Find G'(x). In(9) G(x) = (4e- 7t + 1) dt G'(x) =

A: Given query is to find the derivative of the expression.

Q: find the critical point and classify the function f(x,y) =xlny +x2 -4x-5y+8

A: Answer

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: Let f(x) = x³ + 3x² - 24x + 1 and g(x) = x³ + 6x² − 36x + 1. Fo have critical points?

A: Given,            f(x)=x3+3x2-24x+1    and     g(x)=x3+6x2-36x+1

Q: Suppose f(x) =x++x³ – 6x2. Determine the value of x where f has a relative maximum value. O x= - 2…

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Q: The degree of f(x) is v and the leading coefficient is There are distinct real zeros and relative…

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Q: Find an antiderivative of ƒ(x) = 3x2 that satisfies F(1) = -1.

A: f(x)=3x2, F(1)=-1

Q: The critical point(s) of the function z= 2x²-4xy-2y²+3x-7y+6 is/are...

A: In this question, we need to find the critical points of the function z = 2x2-4xy-2y2+3x-7y+6.