Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of 1%. start with x= 0,1,3 10

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A: Given: f(x) = 4x − 1.8x2 + 1.2x3 − 0.3x4 x0=3, εs = 1% Fomrula used:

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A: Given function is: fx=sin2x-sinx-1   , 0≤x≤2π

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Q: By the use of local linear approximation of g at x=2, estimate g(-1.998) if g(-2)=-1 and g’(-2)=10

A: local linear approximation formula for g(x)g(x)=g(a)+g'(a)(x-a)

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A: Here, fx=648x2+x3 Take x0=6 and △=1 Iteration 1) k=0 of xk Now, xk+1=xk+2k△ Here, x0=6…

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Q: Find the absolute maximum and minimum values of f(x)= ln(x^2+3x+15) on the interval [-2,1]

A: We find f'(x) using chain rule

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

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A: It is given that, f(x)=ln(x2+10x+16)   over the interval 0,4we have to find absolute minimum and…

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A: Given function is: fx=e-x22 Differentiating f(x) with respect to x we get, f'x=e-x22×-2x2f'x=-xe-x22…

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A: In the given question we have to find linearization of function.

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A: First we see a formulaFormula:Newtons divide difference interpolation formulafx=fx0+x-x0 f…

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A: Given the function fx=5sin2x-2x2-4x. The initial guesses are x1=0, x2=1, x3=1.5. The Quadratic…

Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

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Q: Find the maximum of f(x) = 30x4 − 121x3 + 60x2 + 64x USING Newton’s method (x0 = 4, εs = 1%)

A: Given, fx=30x4-121x3+60x2+64x With initial point, x0=4 Differentiating the given equation up to…

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = e−2x ,…

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A: solution is given below..

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

A: It is known by linear approximation that 1+xk=1+kx for the values of x near 0. The given function is…

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Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

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A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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Q: find the marginal revenue of the function. Using the quotient rule.  40x^2 -20x/x^2-10-2

A: Given: Revenue FunctionRx=40x2-20xx2-10-2 To Find: Marginal Revenue Concept: a. Marginal RevenueMx…

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A: Find the minimum of the function f(x) = (X/log X) by using the quadratic-interpolation method with…

Q: Find the critical points that belong to the interval, as well as the absolute minimum and maximum…

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Q: Find two numbers x and y with x-y = 20 for which the term xy is minimized.

A: In this problem, we have to find the two numbers "x and y"