In working on the conceptual design of the new database, Ken determines that the "office" field in one of the tables must includ
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Answer:
The interval over which the graph is decreasing is;
(-∞, -3)
Explanation:
The given function is f(x) = 2·(x + 3)² + 2
By expanding the function, we have;
2·x² + 12·x + 20
From the characteristics of a quadratic equation, we have;
The shape of a quadratic equation = A parabola
The coefficient of x² = +2 (positive), therefore the parabola opens up
The parabola has a minimum point
Points to the left of the minimum point are decreasing
The minimum point is obtained as the x-coordinate value when f'(x) = 0
∴ f'(x) = d(2·x² + 12·x + 20)/dx = 4·x + 12
At the minimum point, f'(x) = 4·x + 12 = 0
∴ x = -12/4 = -3
Therefore;
The graph is decreasing over the interval from -infinity (-∞) to -3 which is (-∞, -3)
Please find attached the graph of the function created with Microsoft Excel
The graph is decreasing over the interval (-∞, -3).
OLTP ( On-line Transaction Processing )
As the name suggests, this system is designed for handling transactions on web applications.
Examples include Banking system.
OLAP ( On-line Analytical Processing )
As per the name, this system is developed for analyzing and reporting functions for web applications.
These systems form a part of data warehousing.
Examples include data mining for Banking system.
OLTP databases undergo ETL operations to form a part of OLAP system. Data from several OLTP database are extracted as per the requirements, transformed ( formatted and cleaned ) to fit the OLAP requirements, and loaded into the OLAP system.
Similarities
• Both OLTP and OLAP are designed for online processing and support web based applications.
• In both systems, processing is done on large scale owing to their online presence.
Differences
• OLTP is designed to handle daily operation. OLAP is designed for decision support.
• OLTP supports data update and data insert operations. OLAP supports data analysis.
• OLTP supports insert, update and delete operations only. OLAP supports data extraction to support decision making process.
• Transactions form the source of data. Several OLTPs form the source of data.
• In OLTP, transactions are shorter in nature. In OLAP, transactions are longer.
• In OLTP, processing time is shorter. In OLAP, processing time is longer.
• Data modification queries are simpler. Data analysis queries are complex in nature.
• OLTP are normalized up to third normal form. OLAP are not normalized.
• Data in OLTP system are frequently modified. Data in OLAP systems are not frequently modified.
• OLTP should maintain data integrity. Data integrity in OLAP is unaffected.
• OLTP stores only current data. OLAP stores historical data.
• OLAP systems must have periodic back up. OLTP back up is achieved by reloading the databases.
The major differences are discussed above to clarify the functioning of both the systems.
