Calc Midterm 2

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jazzybeatle
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67651
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Calc Midterm 2
Updated:
2011-02-21 13:43:28
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calculus reiber
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  1. cost function is the sum of what?
    fixed costs + variable costs
  2. revenue function is the product of what?
    x(p(x))
  3. profit function is the subtraction of what?
    r(x)-C(x)
  4. marginal =?
    derivative of function
  5. marginal cost is?
    C'(x)
  6. marginal revenue is?
    R'(x)
  7. Marginal profit is?
    P'(x)
  8. elasticity of demand =?
    -p(f'p)) / f(p)
  9. Elasticity of Demand Ex.:
    p= -.02x+400
    • 1. find x -> f(p)=-50p+20000
    • 2. find f'(p) -> -50
    • 3. input values in elasticity -> (-p)(-50) / -50p+20000
  10. for E(p) = 50p / -50p+20000 calculate 100 & explain what it means
    • 1. 50(100) / -50(100)+20000 =.33333
    • 2. Means when price is $100 a 1% increase in price will cause .33% decrease in sales
  11. When is demand elastic?
    if E(p) > 1
  12. When is demand unitary?
    if E(p) = 1
  13. When is demand inelastic?
    if E(p) < 1
  14. what happens to revenue if E(p) > 1
    revenue is decreasing as prince increases
  15. what happens to revenue if E(p) <1
    revenue increases
  16. what happens to revenue if E(p) =1
    no change
  17. how do you determine the domain of a function?
    logically figure the numbers that will not =0
  18. how do you find critical numbers of a function?
    take derivative & set it equal to zero
  19. 2nd derivative test
    take the 2nd derivative of function & set it equal to zero to get relative max & min, then plug max, min & domain into original function
  20. what does: f'(c) = 0 & f''(c)>0 indicate in relative extrema?
    f(c) is relative minimum
  21. what does: f'(c) =0 & f''(c) <0 indicate in relative extrema?
    f(c) is relative maximum
  22. what does: f'(c) = 0 & f''(c) = 0 indicate in relative extrema?
    inconclusive, use first derivative test
  23. extreme value theorem:
    if a function f is continuous on a closed interval [a,b] then f has both an absolute max & min value on [a,b]
  24. what value does maximum/minimum refer to?
    y value
  25. how do you make first derivative sign chart?
    • 1. find critical # by solving for DNE or 0
    • 2. have intervals before & after critical #
    • 3. pick number in interval & plug into original function, indicate whether + or - which = increasing or decreasing
  26. how do you make second derivative sign chart?
    • 1. find critical # by solving for DNe or 0
    • 2. have intervals before & after critical #
    • 3. pick # in interval & plug into 2nd derivative, indicate whether + or - which = happy or sad face.
  27. what is an inflection point?
    where concavity changes, in sign chart when 2nd derivative = 0
  28. what does the inflection point mean in terms of revenue?
    tells when the return on money is the greatest
  29. how do you find absolute extrema on open interval w/ 1 critical #?
    • 1. find the critical # in (a,b)
    • 2. Use 2nd derivative to see if the ritical # gives a relative max or min -> f''(c) >0 = abs min & f''(c) <0 = abs max
  30. what are the steps to solving geometric optimization?
    • 1. draw pic
    • 2. assign variables
    • 3. equation to relate variables
    • 4. function in 1 variable & interval
  31. weekly demand for photocopying machine is: p=2000-.04x on (0<x<50000) p is wholesale unit price in $ & x is quantity demanded. Weekly total cost us: C(x)=.000002x^3-.02x^2+100x+120000 where C(x) is total cost incurrend in producing x units
    1. find the revenue function & profit function
    • 1. R(x)= p(x) ->(2000-.04x)x ->2000x-.04x^2
    • P(x)= R(x)-C(x) -> 2000x-.04x^2-(.000002x^3-.02x^2+1000x+120000) -> -.000002x^3-.02x^2+1000x-120000
  32. 2. find the marginal revenue function & marginal profit function
    • marginal revenue: R'(x) =200-.08x
    • marginal profit P'(x)=.000006x^2-.04x+1000
  33. 3. what is the total profit for 5000 copiers? what is the profit from the 5000th copier?
    • P(5000) = $4,130,00
    • P(5000) -P(4999) = $650.05
  34. how do you find the price of the 100th, 200th, 300th, etc. item?
    P(x) for the 100th - P(x) for the 99th

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