Please assist me with the following practice assignment for mathematical economics

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7. i) ii) Assignment 1 — Intermediate Mathematical Economics II All steps must be shown to earn all marks . Apply the quotient rule to compute the derivatives of the following functions. 3 X5 f (x) = E 31+2 f(x) : 2x—1 _ 5 f(x) = :_:2 (10 marks) Use the most appropriate approach to compute the derivative of the following functions. f(x) = lei/FL WMW—s f(x) = 4(8x + x3)4 f(x) = (2x + 2x5);r5 (10 marks) Distinguish between Maclaurin series and Taylor series approximation (2 marks) Find the third order Maclaurin series for each of the following function (12 marks) f (x) = #42: + 4 3 h(x) — 2x+1 1 Approximate the function g(x) = by third degree polynomial at x = 1 (6 marks). (1+:Ic)2 Compute the first and second derivatives of the following functions. From your results, state whether the functions are increasing/decreasing and the rate at which they are increasing/decreasing. What is the curvature of the function (10 marks) h(w) = 2w — 4W3 g(w) = 20 — 2w + 12w2 + 13w3 Compute the partial derivatives of the quadratic function below. Express the derivatives a matrix form and use the Hessian determinant to describe the sign definiteness of the function. (10 marks) f(X.y.z) =34:2 +3!2 + 322 + ny— 4x2— 6312 All global extrema are local extrema, but not all local extrema are at the same time global extrema. State if this is true or false and illustrate (5 marks) Suppose the following functions are differentiable, find the extremum points and use these points to show whether the function is a relative maximum or minimum (10 marks) f (x) = x3 + 12x f(x) = 3x3 — x2 + 7x + 38

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