8. Find the derivative of each of the following functions. (6 points each)
(a)
f
(
x
) = (2
x
3

4
x
+ 8)
6
(
π
2
+ 2 ln(
x
))
(b)
g
(
x
) = 3
5
√
x
+ 4
x

10
+ 2
x
(c)
h
(
x
) =
12
.
5
1 + 48
e

0
.
5
x

16
3
x
6
5
MATH 1231 Final Exam Fl2012
Name:
9. The functionB(t) = 5000(1.035)tgives the balance in dollars in a savings accounttyears after January 1, 2000.(a) (3 points) Find the average rate of change of the balance in the account between January 1, 2005and January 1, 2010. Show work. Give your answer using appropriate units, rounded to two decimalplaces..(b) (3 points) Write a formulainvolving a definite integralthat gives the average balance in dollars inthe account between January 1, 2005 and January 1, 2010.Use proper notation for the definiteintegral, notfnInt.(c) (2 points) Use your formula in part (b) to find the average account balance (in dollars) betweenJanuary 1, 2005 and January 1, 2010. Show work. If you usefnIntshow this. Round your answerto the nearest cent.(d) (3 points) Write a complete sentence with units explaining the practical meaning of the followingstatement:integraldisplay105dBdtdt= $1114.56.Do not use any technical terms from calculus likeintegralorderivativein your answer. Be brief (25words or less) and precise.
6
MATH 1231 Final Exam Fl2012
Name:
10. (5 points) A company produces bracelets for a fundraiser. The profit, in dollars, from selling bracelets isgiven by the functionP(x) = (x10)(500xln(3x))when the selling price of each bracelet isxdollars.Carefully enter the functionP(x) intoY1on yourcalculator.Check that you’ve entered the function correctly by computingP(30). You shouldobtain 7300.114198.Based on past experience with fundraisers, the company expects the selling price of a bracelet to bebetween $20 and $80. UsenDerivand your calculator to determine the price of a bracelet that maximizesthe PROFIT.Write the answer with all the decimal places the calculator gives.Calculator answer:11. A company makes personalized baseball caps.The company has kept a record of its costs for selectedhourly production levels. This information is given in the table below.x= number of hats produced102030405060