4808pset2

4808pset2 - revenue b find the profit equation and the...

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Economics 4808 Problem Set #2 1. Where is the following function discontinuous? 6 x x 5 x ) x ( f 2 - - - = Find the limit: 2. ) 1 x ( 2 x 3 x lim 2 1 x - - + + - 3. lim x x x → - - - 3 3 3 4. h x f h x f h ) ( ) ( lim 0 - + if x 6 x ) x ( f 2 + = 5. Find f’(x) if 2 3 ) 4 ( 1 ) ( + = x x f 6. Find f’(x) if 2 ) 2 ( 1 ) ( + + = x x x f 7. Find f’(x) if 2 3 ) 1 x 6 ( x 2 ) x ( f + = 8. Find f’(x) if 4 2 3 ) 7 2 ( ) ( - + = x x x f 9. Find f’(x) and the equation to the line tangent to the graph at x=3 if 2 2 ) ( - = x x x f 10. Find where the line tangent to f(x) is horizontal if 3 2 ) 2 ( ) 4 2 ( ) ( - + + = x x x x f 11. Find f’(x) both by simplifying and by the product rule when f(x) = x 3 (2x 2 +1).

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Find the derivative: 12. f x e x x x ( ) ( ) = + + 2 4 2 13. f x x x ( ) (ln ) = + 2 1 14. f x e x x ( ) ln ( ln ) = + 2 15. x 4 2 e ) 2 x ( ) x ( f + = 16. The total cost and price (in dollars) for the production and sale of x hats are given by a. find the revenue equation and the amount of hats the company must produce to maximize
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Unformatted text preview: revenue. b. find the profit equation and the amount of hats the company must produce to maximize profits. 17. If the price of a good is given by: x ln 4 p-= and they cost \$1 a piece to make. What price will be charged when profits are maximized? 18. If the price of a good is given by: x x e x p ) 1 ln 3 ( 10 + +-= and costs are given by: x x xe x C ) 1 ln 3 ( ) ( + = How many should be sold to maximize profits? 19. Given the demand equation: p = 1000e-0.02x Find the marginal revenue equation. x x p and x x C 4 . 40 ) ( 100 16 ) (-= + =...
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4808pset2 - revenue b find the profit equation and the...

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