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### Problem 16

Find the $x$ -value of all points where the functions defined as follows have any relative extrema. Find the value(s) of any relative extrema.
$$f(x)=x^{3}+3 x^{2}-24 x+2$$ Matt J.

### Problem 3

Give the general expression for the equilibrium constant of the
following generic reaction: William M.

### Problem 16

Find the $x$ -value of all points where the functions defined as follows have any relative extrema. Find the value(s) of any relative extrema.
$$f(x)=x^{3}+3 x^{2}-24 x+2$$ Matt J.

### Problem 1

In June 2009, at the trough of the Great Recession, the Bureau of Labor Statistics announced that of all adult Americans, 140,196,000 were employed, 14,729,000 were unemployed, and 80,729,000 were not in the labor force. Use this information to calculate:

b. the labor force

c. the labor-force participation rate

d. the unemployment rate Yi Chun L.
Washington University in St Louis

### Problem 25

Find the Taylor series for $f(x)$ centered at the given value of $a.$ [Assume that $f$ has a power series expansion. Do not show that $R_n (x) \to 0.$] Also find the associated radius of convergence.

$f(x) = \sin x,$ $a = \pi$ Amy J.

### Problem 98

The nuclide 18F decays by both electron capture and b+ decay. Find the difference in the energy released by these two processes. The atomic masses are 18F = 18.000950 and 18O = 17.9991598. Monica Mame Soma N.
Michigan Technological University

### Problem 9

9. Purchasing-power parity holds between the nations of Ectenia and Wiknam, where the only commodity is Spam.
a. In 2015, a can of Spam costs 4 dollars in Ectenia and 24 pesos in Wiknam. What is the exchange
rate between Ectenian dollars and Wiknamian pesos?
b. Over the next 20 years, inflation is expected to be 3.5 percent per year in Ectenia and 7 percent per
year in Wiknam. If this inflation comes to pass, what will the price of Spam and the exchange
rate be in 2035? ($Hint:$ Recall the rule of 70 from Chapter 27.)
c. Which of these two nations will likely have a higher nominal interest rate? Why?
d. A friend of yours suggests a get-rich-quick scheme: Borrow from the nation with the lower nominal interest rate, invest in the nation with the higher nominal interest rate, and profit from the
interest-rate differential. Do you see any potential problems with this idea? Explain. Jesse N.

### Problem 77

Where should the point $P$ be chosen on the line segment $AB$ so as to maximize the angle $\theta$?

WZ
Wen Z. 