Derive a 2nd order accurate finite difference expression for the first derivative at point i-1, using the values at points i and i+1, in the case of general (non-uniform) spacing. Then reduce this expression in the case of uniform spacing Use polynomial fitting

Q: at point x0=1 ,x1=1 and x2=2 f(x)=sin(x)+(x^2)+xe^2 function crossing second Write down the…

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Q: Let f(x) = x² – 8x – 14 Use the second derivative test to find any local maxima and minima. First,…

A: for critical value put first derivative zero if second derivative positive minima and if negative…

Q: Find the derivative of the polynomial using Numerical Differentiation of forward finite divided…

A: Given: The polynomial in the form of text Four hundred multiplied by variable "x" raised to the…

Q: (b) Verify Mean Value Theorem for f(x)= 3x2-6x -5 over the interval[-1,4].

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Q: Find any critical numbers for ƒ and then use the second derivative test to decide whether the…

A: Given, ƒ(x) = x2 - 12x + 36 To find critical points of the above function and find the relative…

Q: Use the second order derivative test to find local exterma of the function  f(x) =x3-9x2-48x+72 on…

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Q: 4. Use the first derivative test to find the intervals of increase and decrease, and the relative…

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

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Q: Write an equation of a polynomial, f, such that the second derivative test fails to determine if f…

A: Let f(x) = x3

Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: Use the second derivative test todetermine whether f(x)=-2x³+6x2-3 has a localmaximum or…

A: Given,          fx=-2x3+6x2-3

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

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

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A: Given function f(x)=3+12x-x2 To find critical points we need to differentiate the function f'(x)=0…

Q: 2. Use the second derivative to determine the intervals where f(x) = -2x³ + 4x2-150x is concave up…

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Q: (b) Verify Mean Value Theorem for f(x)= 3x² – 7x – 4 over the interval[–1,4] .

A: Given: fx=3x2-7x-4

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

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: Use the First Derivative Test to locate the x-value of all extrema. Classify if it is a relative…

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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: 6. Find all critical numbers and use the Second Derivative Test to determine all local extrema. a)…

A: for part a see 2nd step. for part b see 3rd step.

Q: 3. Determine the intervals of concave upward and downward, points of inflection, critical nu bers,…

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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: Use the Linear Approximation to estimate Af for f(x)=, when a = 2 and Ax = - !. 2412 (Use decimal…

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Q: Assume that f is a polynomial and x = 10 is a critical number for f If f''(10) = -sqrt2 what do we…

A: A function y = f(x) has a critical point at (x, y) if f'(x) = 0 or f"(x) is not defined. But as we…

Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: Use the second derivative test todetermine whether f(x)--+ 18z has a localmaximum or localminimum at…

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: Determine the critical numbers of the ff. functions.

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Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

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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…

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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: In exercises 9–14, find all critical numbers and use the Second Derivative Test to determine all…

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Q: Compute f'(3) using the limit definition of derivative if f

A: Given: f(x)=6x2f'(3)

Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: Find thu constant a such that the function 15 Continuous on thi entire real line. Usinx gex)= a-7x…

A: Here we use the concept of limit

Q: Find the critical points of f(x) = -x²-3x + 3. Identify the intervals on which f is increasing and…

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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: find all critical points of f and use the First Derivative Test to determine whether they are local…

A: Consider the function

Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

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Q: Use second derivative test, If f(x) = 36x + 4 then f(x) has a local 3 maximum at the point O x = -7…

A: Here we need to find the local maxima of the function.  The solution is following .

Q: What is the second iterative value of the root f(x) = x2 - 3.  with the initial bracket [1, 2] using…

A: To find- What is the second iterative value of the root fx = x2 - 3 with the initial bracket 1, 2…

Q: Show that the equation x - 17x +c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x…

A: The given equation is : fx=x3-17x+c The given equation has at most one solution in the interval…

Q: prove that f(x)=3x^3-4x^2-x-3 is continuous over [-3,3]

A: Since you have submitted two questions, we'll answer the first question. For the second question…

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: 2. Use the First Derivative Test with a number line to find the local extremes of the function Ax) =…

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Q: Use the First Derivative Test to find the x-value(s) at which the function 4 f(x) = x4 - 4x² + 1 X.…

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Q: 4. Assume that æ € [0, 1] and write the error in the approximation to the error function using the…

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