Final answer:
Calculators can calculate intervals of increase and decrease but do not take into account significant figures, requiring the user to assess the accuracy of the results. Technology aids in performing complex calculations, yet understanding the manual steps remains important for a deeper mathematical understanding.
Step-by-step explanation:
Intervals of increase and decrease can be calculated using a variety of technologies, including calculators. When performing calculations, it's important to remember that calculators provide an answer based on the input without considering the accuracy or significant figures. For instance, multiplying or dividing two numbers can give you a result with more decimal places than the accuracy of the numbers warrants, and the user must decide how many decimal places to report.
Technological tools such as computer spreadsheets, statistical software, and advanced calculators can facilitate calculations, such as finding the best-fit line, creating scatter plots, and computing confidence intervals. Specific models like the TI-83, TI-83+, and TI-84+ calculators have built-in functions to aid in these computations. However, for understanding the underlying mathematics, a step-by-step solution (Solution A) is often beneficial alongside the calculator's shortcut (Solution B).
While calculators are powerful tools, it's crucial to assess the reliability of the data and the accuracy of the results. Especially in educational settings, educators encourage students to understand both manual methods and the use of technology to ensure a deeper grasp of mathematical concepts and their applications.