TI-Nspire CAS in Engineering Mathematics: Highest Temperature in a Disk
Find the maximum of a two variable continuous function. Using Lagrage multipliers and parametric equations. Connecting single and multivariable calculus.
Multivariable calculus textbooks contain many impressive figures showing the geometrical interpretation of Lagrange multipliers. Our goal in this document is to use TI-Nspire CAS to find the maximum value of a two variable continuous (polynomial) function over a closed bounded disk.
We first locate the interior points and make the analysis, using the second derivative test. Because our example hopefully does not require implicit plotting, we also animate level curves of the temperature function. This yields a good idea of where, on the circular boundary, the maximum value is achieved.
Then two methods are used to find algebraically this extreme value on the boundary: Lagrange multipliers and parametric equations. Connecting single variable calculus and multivariable calculus is a good idea.