Math Review 3 - MATH AND CALCULUS REVIEW EXERCISES The...

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MATH AND CALCULUS REVIEW EXERCISES The following questions are to help you review exponentials, derivatives, partial derivatives, optimization, and constrained optimization. 1. a) What is 27 -1/3 equal to? b) What is X 1/2 X 1/3 equal to? c) What is (X 2 ) 3 equal to? d) What is the area of a triangle whose base is 5 metres and whose height is 20 metres? 2. What is the significance of the first order derivative of a function? 3. Find the first order and second order derivatives for each of the following functions: a) Y = 6; b) Y = 6X – 5; c) Y = 6X 3 + 3X 2 ; and d) Y = 6X 1/3 . 4. Using the product rule, find the first order derivative of the following functions: a) Y = 5X 4 (3X - 7); and b) Y = 3X 1/2 (2X 2 + 3). 5. a) A firm's total revenues are R = 200Q - 25Q 2 . What is the first order derivative (with respect to Q)? b) What is the meaning of this derivative? 6. a) Diagram the following function: Y = 5X 2 - 20X + 50. b) At what value of X does Y reach a minimum?
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Math Review 3 - MATH AND CALCULUS REVIEW EXERCISES The...

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