Scientific Calculators: Maxima and Minima
Introduction
This blog entry covers four calculators:
Casio fx-991CW
Casio fx-991EX Classwiz
Texas Instruments TI-36X Pro
Texas Instruments TI-30X Pro Math Print
Here is how to find extremum of any general function f(x) and g(x). This method will tell you where the extremum is located, but not whether the extremum is a minimum or a maximum.
The extremum of a function can be found by finding the root of the function's derivative:
d/dx f(x) = 0
The steps required are:
1. Solve d/dx f(x) = 0 to get x.
2. Calculate y. This is easier if we can store the function in f(x) or g(x).
Two methods to find the x point of extremum:
1. Extremum using f(x) (or g(x))
2. Extremum using direct entry method
The example used is to find the extremum of e^(sin x) with an initial guess x=1. We'll be focusing on the x point only.
Casio fx-991CW
Either method can be used. In the Solver Mode, the function button ( [f(x)] ) is available to define f(x) (or g(x)). Since we are finding a root, we don't have to include the "=0" at the end.
The equation to be used in the solver is:
d/dx( f(x) ) | x = x (MathIO input)
f(x) can be referenced or typed directly, like:
d/dx( e^(sin(x)) ) | x = x
Casio fx-991EX Classwiz
The direct entry method must be used. The accuracy may vary for the last digits. Not as accurate as the fx-991CW.
Note: Extremum for quadratic and cubic equations (fx-991CW only) are automatically calculated through the Solver-Polynomial feature of both the fx-991CW and fx-991EX.
Texas Instruments TI-36X Pro and TI-30X Pro MathPrint
Either method can be used. f(x) (and g(x) for the TI-30X Pro MathPrint), is edited through the [table] key. When the function is edited, press [ 2nd ] [ mode ] (quit) to exit the table. To enter Numeric Solver Mode, press [ 2nd ] [ sin sin^-1 ] (num-solv).
The solver has the format:
[ ] = [ ]
In this case, we will need to include the 0 on either side of the template.
Finding extremum is fairly simple.
For the example, the extremum e^(sin x) around x = 1 is x = π/2 (≈ 1.570796327).
Eddie
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