business calculus

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Author:
jillmray
ID:
82706
Filename:
business calculus
Updated:
2011-04-29 17:55:07
Tags:
test review
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Description:
lesson 14-22
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  1. river optimization problem
    1500 meters of fencing divided pasture into two parts that runs along the river and you wish to find the max possible area. What are the steps?
    • 1) A=xy
    • 2) 1500 = 3x+y then set equal to y
    • 3) plug y= -3x+1500 into A=x*y
    • 4) find the derivative of A(x)
    • 5) set A'(x) equal to zero and solve this is the length
    • 6) find the second dervative
    • 7) answer must be negative since its a max
    • 8) find the width plug in x into
    • original function y= 1500- 3x
    • multiply both
    • 8) find the width
  2. postal regulations girth plus length can be no more than 104 inches find the maximum volume and dimensions for this package
    • 1) 104= 4x + y
    • 2) V= lwh or xxy or x^2y
    • 3) sub y= -4x+104 into x^2y
    • 4) find the derivative
    • 5) set the derivative V'(x) equal to zero and solve
    • 6) test with the second derivative answer should be negative since max
    • 7) plug in the length & width (x) into the original function -4x+104 to get (y) the height
    • 8) multiply XXY to get the volume
  3. a farmer has 384 feet of fencing for 2adjacent regtangular pens. what is the max area?
    • 1) 3x+2y = 384
    • 2) Area = xy
    • 3) plug in y= -3x+192 into xy
    • 4) find the derivative of A(x)
    • 5) set A'(x) equal to zero and solve
    • 6) use second derivative test to check for max
    • 7) plug in x into the original function
    • -3/2x+192 which will give you y
    • 8) multiply xy for area
  4. population in beginning was 2mil after 3 years it inc to 5 mil what will be the pop in 9 years with exponential growth
    • 1) exponential growth forumula
    • Q(t)= Qoe^kt
    • 2) 5mil = 2 mil e^k(3)
    • 3) divid both sides by 2
    • 4) put ln on both sides to get rid of e which leaves you with
    • ln2.5= 3k
    • 5) divide ln2.5 by 3 to get k
    • 6) plug k into the function 2e^k(9)
    • (side note multiply power k(9) then plug into e then multiply times 2)
  5. solve the initial value problem
    f(x)= 3x^2 + 6x -1
    f(1)= -6
    • 1) find the antiderivative of the function
    • 2) plug in 1 for y and -6 for x
    • 3) solve for c
  6. x^2
    x^3 - 4

    find the indefinate integral
    • 1) let u = x^3 - 4
    • 2) find the derivative of the right side
    • 3) gives you du = 3x^2
    • 4) you only need x squared so divide both sides by 3x
    • 5) then substitute 1/3 * 1/u

    • 6) substitute the bottom of the function into the integral
    • 7) gives you 1/3 ln(x^3-2) + c
  7. find the average value of f(x)= 18x^2+3
    over the interval [-2, -1]
    • 1)
    • 1
    • ____ ( integral of f(x))
    • -1- -2

    2) 1 [ f(-1) - f(-2)]

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