Use a Lagrange interpolating polynomial to approximate the derivative of the function tabulated below as follows: • (a) Determine the quadratic (2nd order) Lagrange polynomial, f2(x), through the points tabulated on the left for the function, f (x). (b) Determine the derivative of the polynomial, f(z). i *; f(x:) 0 -h_fo dz • (c) Use the result of (b) to approximate the derivative of the function, f (x), at x=L, =0: f(x) ~= 5:(x). Write the approximation in a form that lets dz dz h f2 you recognize the answer to (d) below. (d) What is the name of the result obtained in (c)? 2)

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(s) =…

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Q: R(w) = w? 8w + 20

A: Derivatives are one of  the fundamental tools of the calculus. In mathematics, derivatives are the…

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

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Q: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.