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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)]
 Author: jillmray ID: 82706 Card Set: business calculus Updated: 2011-04-29 21:55:07 Tags: test review Folders: Description: lesson 14-22 Show Answers: