# final - Name Math 160 Final Exam Business Calculus Part I 1...

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Name: ________________ Math 160 Final Exam Business Calculus Part I 1. Limits and Continuity g x = { x 2 5 x 6 x 2 2 x 3 x 3 a x = 3 What value of x makes g continuous at x = a ? Using this value for a , is g continuous everywhere? (i.e., are there any other discontinuities?) 2. State the definition of derivative for the function f ( x ): f '( x ) = Use this (i.e., the four step process) to find the derivative of the function f x = x 2 2 x 1

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3. Using your answer from #2, what is the equation for the line tangent to this function at x = 0? Part II: 4. Find the derivative: P x = x 2 ln x f x = e x x 2 1 5. A car rental agency rents 200 cars per day at a rate of \$30 per day. For each \$1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income? Rate: __________ Maximum income: ______________
6. For the function f x = x 3 3 x 2 9 x A. What are the critical points for this function?

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final - Name Math 160 Final Exam Business Calculus Part I 1...

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