Final answer:
The process of finding critical points for a function with two variables using a TI-83, TI-83+, or TI-84 calculator includes entering the function, graphing, solving for zeros, and analyzing the derivatives to identify critical points.
Step-by-step explanation:
Finding critical points for a function with two variables involves identifying points on the graph at which the first derivative is zero (or undefined) and does not change sign. The steps to find critical points using a calculator, specifically a TI-83, TI-83+, or TI-84, include:
- Entering the function into the calculator.
- Using the graph function to visualize the function's behavior.
- Determining the zeros of the function by solving the equation U(x) = 0 for critical points.
- Examining the first and second derivatives to identify extremes and confirm critical points.
When the graph of a function is tricky to interpret, additional strategies such as zooming in may be helpful. For certain functions, sketching diagrams showing substitution and income effects with correct points of tangency can be utilized to find critical points as well.