Let p(x) be a polynomial function of degree n with simple roots r1,..., xn. Show that ) p"(x;) = 0. p'(x)

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A: We know that linear approximation (by using the tangent line to f(x) ) of f(x) at point (a,f(a)) is…

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

Q: Find local maximum or local minimum of f(x)= -sin 2x -x defined on 22

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A: Topic:- limits and calculus

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

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A: The second order taylor polynomial of a function fx centered at the point a is defined as follows:…

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Q: Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

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Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: 1. Determine where f(x) = arcsin (x² – 2x) is increasing. %3D

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Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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Q: 2. Compute for a real root of sin -x 0 using three iterations of Fixed- Point Iteration Method with…

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Q: 2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's…

A: Consider the given function,

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Q: Apply the secant method to solve f(x) = e** In x² – x = 0. Discuss the procedure for dealing with…

A: We are given the following function.  f(x)=ex2lnx2-x=0. We have to solve by the secant method. Note…

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

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Q: Consider a function f with domain {x|x # 0} and the following derivatives: f'(x) = bx-1 and f"(x) =…

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Q: The value of the function f(x) and some order derivatives at the point x=1 are given in the…

A: Given table with derivatives

Q: Find the interpolating polynomial for the function f(x) = e through the points x = 0, 1, 2.…

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Q: a. Find a cubic polynomial with equation y = ax' + bx whose tangent line at (2, -6) is y=-19x+32.…

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Q: Prove that f(x) =- 2x(sinx+ tanx), is an odd function, where [] denotes %3D X+ 2n -3 the greatest…

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Q: 4th degree polynomial of y=sinxcosx centered at x=pi

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Q: Use Taylor's polynomial of degree 2 of the function f(x) = tan 1(x+1) + x² %3D about c = - 1 to…

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Q: Find the local quadratic approximation of f at x = x0, and use that approximation to find the local…

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Q: 1 The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cose

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Q: Derive a 2nd order accurate finite difference expression for the first derivative at point i-1,…

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Q: 5. Find the absolute minimum and absolute maximum values of f(x)= 2cosx +sin2x on the interval 2 N

A: Consider the given function,To find the absolute minimum and maximum values of the given function,…

Q: The value of the function f(x) and some order derivatives at the point x=1 are given in the…

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Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: Differentiate the Maclaurin polynomial of degree 4 for f(x) = ex . Describe the relationship between…

A: Maclaurin polynomial of degree 4 is P4x=f0+f'0x+f''02!x2+f'''03!x3+f404!x4.

Q: A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a…

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Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line…

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Q: 15. For this function find the coordinates of points on the graph that are local maximums or…

A: Local maxima and minima

Q: The 4th degree Taylor polynomial for sin(x) centered at a = is given by 6 V3 3 sin(x) = X - 48 +…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: Show that the nth Maclaurin polynomial of f (x) = arcsin x for n odd is 1.3 x Tn (x) = x+ 23…

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Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…

Q: Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5.…

A: Since, function is not clear so we assume fx=1x. We have to find the Newton's polynomial that…

Q: Consider a differentiable function f with domain R and derivatives f'(x)=-aebx(1+bx) and…

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Q: Let -(x) be the Taylor polynomial of degree for the function x) = cos(x) at = 0. Suppose you…

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Q: 7. Verify the validity of the Mean Value theorem of Lagrange in the case of f(x) = 2x3 – x +1 in the…

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Q: Approximate cos⁡(−0.3) with a Maclaurin polynomial of degree 2. (Enter either an exact answer or at…

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Q: Show that a nonzero polynomial function y = f(x) cannot sat- isfy the equation y" = -y. Use this to…

A: given equation is  y"=-y

Q: Find the critical numbers for f(x) = sin2xcos2x

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