For a given function f(x), the divided -differences table is given by: X, = 1 X, = 2 X, = 3 f[xo] = 0 f[x,] = 7 f[x2] = 26 f[x9,x,] = 7 f[x1,x2] = 19 f[xo,x1, xz] = 6 An approximation of f(2.75)is: O 2 O 4 O 20.125 O 15

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: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the…

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Q: For which value of x does the Maclaurin polynomial Tn satisfy Tn(x) = f (x), no matter what f is?

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Q: Given f (x) =r - 4r defined over [1, 3]. Using Secant :method, the first approximated root for f(x)…

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Q: 16. If f(x) = 2x² + 3x + 5, f(c) = 20, and the interval is [0,5], use the Intermediate Value Theorem…

A: If fx=2x2+3x+5,  f(c)=20,  [ 0,5]  f0=202+30+5 = 5  f5=252+35+5 = 70  Using Intermediate value…

Q: 1) For the function f(x)=10-0.1x² +1.6x² – 4.8x on 0<x<10 and n=5: Begin by calculating Ar and…

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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 critical points of the function f(x) = 36a – 2a4 occur at z= 0, z = +3.00 x = 0, x=±12.00 O r=…

A: We have to find critical points

Q: Given the function y=f(x), y" is found to be negative over the interval (4,8), then over this…

A: Answer is given in next step.

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: Consider the region bounded above by f(x)=−6x^2−50 and below by g(x)=−5x^2−19x+40. Find the area, in…

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Q: Find the critical numbers of the function f(z) = 2x'-24r. Answer (separate by commas): I = Il

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Q: ) If we apply Rolle's Theorem to the function f(x)=2x^2−8x−4 on the interval [0,4], how many values…

A: Given: fx=2x2-8x-4 on the interval 0,4 To find the value of C using Rolle's Theorem.

Q: 2. For the given functions f (x), let.x, = 1,x, = 1.25, and.x, = 1.6. Construct interpolation…

A: Step:- 1 Lagrange Interpolating polynomial:- P(x)=f0 L0(x) +f1 L1(x)+ f2 L3(x)+....fn Ln(x),Here,…

Q: If we apply Rolle's Theorem to the function f(x) = 2x2 – 16x – 4 on the interval [2, 6], how many…

A: We state Rolle's theorem here ------    Let f : [a,b] -&gt; R be a function continuous on [a,b] and…

Q: Given the points x, = 0,x, 1 and x, =3 and let f be a function such that f(x) =-1, f(x) = 1 and…

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Q: 2. For the given functions f(x), let Xo 1,x 1.25, and.xy = 1.6. Construct interpolation polynomials…

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Q: The critical points of the function f(x) = 16x2 - 2x occur at O r= 0,x =±1.00 O r= 0, x =±1.60 O r=…

A: Solution is given as below:

Q: OO O Consider the regular subdivision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with…

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Q: 4. For the given function f(x) = /2 + x², let xo = 0, x1 = 0.5, and x2 = 0.8. Construct a Lagrange…

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Q: For f'(x) = (x – 7)(x + 1)(x + 5), Find (i). What are critical points of function (ii). On which…

A: Given,            f'(x) = (x - 7) (x + 1) (x + 5)

Q: Consider the regular subdivision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with the…

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Q: The critical points of the function f(x) = 9x² – 2xª occur at %3D O x = 0, x = ±0.75 O z = 0, x =…

A: Given: fx=9x2-2x4

Q: Consider the function f(x) = 8(x – 2)³. For this function there are two important intervals: (- 00,…

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Q: f(x) = x3-3x2+3x-1 ;   m = -1   ;  [-1, 2]

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Consider the regular subdivision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with the…

A: According to Simpson's rule, if the interval a , b is divided in to n equal sub intervals then the…

Q: Consider the regular subdivision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with the…

A: Given that fa=fb=1; fx1=1.5; fx2=fx3=2. Let us denote the values of function as  y0=1; y1=1.5; y2=2;…

Q: Find the critical numbers of the function * 4 f(x) = x3 (x + 7)2 0, 2, and 7. 0, 2, and 4.

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Q: For the given functions f(x), let x, = 1,x1 = 1.25, and x, = 1.6. Construct interpolation…

A: PART A The given function is, f(x)=sin πx For x0=1 then f(x0)=0 For x1=1.25 then f(x1)=-0.7071 For…

Q: Consider the regular subdivision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with the…

A: Given

Q: Consider the regular subdrvision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with the…

A: We wre going to composite simpsons rule to approximate the given integration

Q: Consider the regular subdivision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with the…

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Q: Let f(x) = e* for 0 < x<1 a. Approximate f(0.25) using linear interpolation with xo = 0 and x1 = 0.…

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Q: Find the critical numbers of the functions. (3) f(x)= |x-1| 1 (4) f(x)= (x² –x)

A: Critical numbers are those points on the function where its derivative becomes zero or infinite.

Q: Given that f(x)= (1-x^2)/(x^2+1)^2 , find the critical numbers of f .

A: The function is given by fx = 1-x2x2+12 To evaluate : The critical numbers of the function f(x)

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: Determine all critical points for the function. f(x) = 5 бх %3D x+5 O A) x = -5 O B) x = 30 and x =…

A: Here, we need to find all the critical points for the function. We are given the function…

Q: The function f(x) 2x³ 33x² + 108x - 6 has two critical numbers. = The smaller one is x = and the…

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Q: The function f(x) = cos(3x) is interpolated on the interval [О, 1/5] with a polynomial of order 3…

A: According to the given information, Consider the given function.

Q: Consider the regular subdivision of the interval [a, b] as a = x0 < x1 < x2 < x3 < x4 = b, with the…

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Q: 1. For the given functions f (x), let xo = 0, x1 = 0.6, and x2 = 0.9. Construct interpolation…

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Q: 1. For the function f(x) = /1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Con- struct Lagrange…

A: Given:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: To find the critical numbers, first find the derivative of f(x) then set the derivative equal to…

Q: The function f(x) = 13x - In(7x + 14) has a single critical number at x = A. Find this critical…

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Q: Given f (x) = x² – 4x + 9 [1,4] find the critical points on the close interval. 68 F Mostly sunny…

A: The given function is:fx=x2-4x+9To find the critical point

Q: Consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2 −9x−18. Find the area, in…

A: Calculation:The given curves are f(x) = – 9 x – 9 and g(x) = x2 – 9x – 18.The area enclosed by two…

Q: The critical points of the function f(x) = 16z-2x occur at O z=0,r =±1.60 %3| O z= 0,1 = ±8.00 O z=…

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Q: For a given fimction f(x), the divided-differences table is given by: Xo - -2 f[xo] = 2 X1 -0 S[x] =…

A: Here for a given function f(x) , the divided differences table is given. We have to find an…