Let f(x) = x³ + x + 4 and g(x) = 3x + 2 in Zs[x]. Then, upon dividing %3D f(x) by g(x), we get None of these The quotient is 1+3x + 3x^2 and the remainder is 1 The quotient is 6 +x + 4x^2 and the remainder is 0 The quotient is 4+2x+2x^2 and the remainder is 1

Q: The function f(x) = 2x° - 36x + 192x 8 has two critical numbers. %3D The smaller one is x = and the…

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Q: Find the critical numbers of the function.    g(x)=x^4-2x^2+3

A: The given function is g(x)=x4-2x2+3.

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: The function f(x) = 2x – 42x + 270x – 2 has two critical nu The smaller one is x = and the larger…

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Q: Find the critical numbers of the function.   f(x)  = 2x3 + x2 + 2x

A: We find the first derivative using the power rule

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: The integral of the function f(x) = (6x2 + 10x + 2) dx / (x + 3x² + 2x) may be determined by partial…

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Q: In the function:  f(x)= (4x^2)/((x^2)+4)  What are the critical numbers of the function?  Where is…

A: Given function

Q: Q4. Evaluate "by partial fraction' x³ + 3x2 + x +9 -dx (x* + 1)(x² + 3)

A: Consider the given fraction px=x3+3x2+x+9x2+1x2+3. The denominator of the fraction has two factors…

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: The function f(x) 2x 36x + 162I - 7 has two critical numbers. The smaller one is x = and the larger…

A: The critical number of a function f is a number c such that either f'(c) =0 or f'(c) doesn't exist.

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

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Q: For the function f(x) = -2x + 3x2 + 12x 1. Find all the critical points of the function f(x). 2.…

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Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

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Q: The function f(x)=2x^3−36x^2+162x−9 has two critical numbers. The smaller one is x = and the…

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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: The function f(x)=2x^3−33x^2+108x-4 has two critical numbers. The smaller one is x =?    and the…

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Q: Find the critical numbers of the function. f(x) = 3x + 4x3- 12x2 %3!

A: Given function is f(x)=3x4+4x3-12x2. The critical number of a function f is a number c in the domain…

Q: g(x) = V4– x²

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Q: Determine whether the function f(x)= 2x³-3x²-36x+49 is increasing or decreasing at x=5 and x=3. Also…

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Q: (b) Let f(x) = 12x35+ 15x* – 40x³ + 17. Find the critical numbers, and show what the Second…

A: f(x) = (12x 5+15x4 -40x3 +17.   critical points   f'(x) = 0   60 x4 + 60x³-120x²  = 0.   x² ( 60…

Q: giver yn f(५) ५) -2x + 3, + 2, find of ax

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Q: Find all critical points of the function f(x) = x² – 4x + 6 = x

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Q: Find the critical points of the function f(x) = 8x^3 + 4x^2 - 12x + 10 and determine their nature.

A: Solution: Given: f(x)=8x3+4x2-12x+10

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

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Q: Find the critical numbers of the function. f(x) = 5x In x %3D X =

A: The given function,  fx=5x ln x

Q: The function f(x) = 2x 30x2 + 126x 1 has two critical numbers. - The smaller one is x = and the…

A: Solution: the objective is to find the critical numbers of the given function

Q: Find the critical numbers of the function. 3. g(x) = V 25 – x2 X =

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Q: Find the positive critical point of the function f(x) = : 8+6 * x =

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Q: Find the critical points of f(x)=6x-x^2.

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Q: 1. Find all critical points for the functions: a) f(x) = x² – 10x – 9 5 – x b) f(x) = x² – 6x + 30 -

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find the positive critical point of the function f(x)=x/x^(8)+6

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Q: Find the critical numbers of the function.…

A: Critical numbers : f(x)=4x2-6x The derivative of the function is f'(x)

Q: Find all the critical numbers for the function g(x) = ¼ x4 - x3 - 5x2

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Q: The function f(x) = (6x + 3)e-6a has one critical number. Find it.

A: Given: f(x) = 6x + 3 e-6x To find: Critical number  Proof: We will differentiate the function w.r.t…

Q: Using Taylor's theorem, formally represent 2x° +x* – 3x³ +x² – 5x +1 as x+1.

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Q: Find the critical numbers of the function. (Er g(x) = x6 – 3x4

A: To find the critical numbers we first find g'(x) using the power rule

Q: The function f(x)=2x^3−42x^2+270x+8has derivative f′(x)=6x^2-84x+270. f(x) has one local minimum…

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Q: g(x) = x' + 3 x² – 24 x

A: The point x=k is said to be the critical point of the function f(x) if Case 1 : f(k) exists and…

Q: What is the critical point of the function g (x) = (x ^ 2/2) + x (ln (x) −1), using Newton-Raphson,…

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Q: Sketchthegraphofy=x2−5x+4.

A: We first make a table for y=x2 −5x+4 x 1 2 2.5 3 4 y 0 -2 -2.25 -2 0

Q: Find the critical numbers of the function

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Q: Find all critical points for the function f(x)= x²e!-2¤. %3D

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Q: Find all critical points of f(x) = 2x³ + 2x-. (Use symbolic notation and fractions where needed.…

A: First, we find f'(x) using the power rule

Q: The function f(x) = 2x³ − 42x² + 270x – 4 has two critical numbers. The smaller one is x = and the…

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Q: 3/ Find the critical numbers of the function f(x)= x/5 (4-x)

A: The given function f(x)=x354-x

Q: The function f(x)=2x^3−27x^2+48x−6 has two critical numbers. The smaller one is x =   and the…

A: The given function is f(x)=2x3-27x2+48x-6                           Differentiate with respect to x,…

Q: Find the critical numbers of the function. f(x)=32x-2x^2 x=

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Q: he function f(x)=2x^3−36x^2+162^x−7 has two critical numbers. The smaller one is x=    and the…

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Q: Find the critical numbers of the function F(x) = x4/5(x - 8)2 %3D I

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