Question 6

2 pts

The table shows the U.S. city average price of bananas, in cents per pound, for selected months and years. Locate all

relative extreme points or saddle points in the table.

Price of Bananas (cents per pound)

Year

Month

Apr May Jun Jul Aug Sep Oct

2004 50.5 49.1 49.8 51.0 50.7 48.8 48.5

2005 50.3 49.7 49.3 49.4 48.7 48.5 49.1

2006 50.8 51.4 51.1 50.8 49.2 47.9 48.9

2007 51.7 50.3 51.2 50.9 50.6 50.5 50.8

2008 62.7 63.0 63.3 62.7 63.4 63.1 62.9

2009 62.9 62.2 61.7 61.6 61.1 60.5 59.8

In June 2008, the U.S. city average price of bananas was at a

saddle point

In October 2009, the U.S. city average price of bananas was at a

In July 2008, the U.S. city average price of bananas was at a

relative minimum

relative minimum

In September 2006, the U.S. city average price of bananas was at a

relative minimum

To identify the relative extreme points or saddle points in the table, we need to compare the price of bananas for each month with the prices of the neighboring months.

1. Saddle point:

- A saddle point occurs when a point is higher than its neighboring points in one direction and lower than its neighboring points in the other direction.

- In June 2008, the price of bananas (63.3 cents per pound) is higher than its neighboring months (63.0 cents per pound in May 2008 and 63.4 cents per pound in August 2008). Hence, it is a saddle point.

2. Relative minimum:

- A relative minimum occurs when a point is lower than its neighboring points.

- In October 2009, the price of bananas (59.8 cents per pound) is lower than its neighboring months (60.5 cents per pound in September 2009 and 61.1 cents per pound in November 2009). Hence, it is a relative minimum.

- In July 2008, the price of bananas (63.4 cents per pound) is lower than its neighboring months (63.0 cents per pound in June 2008 and 63.1 cents per pound in August 2008). Hence, it is also a relative minimum.

- In September 2006, the price of bananas (47.9 cents per pound) is lower than its neighboring months (50.8 cents per pound in August 2006 and 48.9 cents per pound in October 2006). Hence, it is a relative minimum.

So, the identified points are:

- Saddle point: June 2008

- Relative minimum: October 2009, July 2008, September 2006