A derivative is a function that measures the rate of change of another function at a given point. It is often denoted by the symbol f'(x) or dxdy, where y=f(x). Finding derivatives on a ti-89 calculator can be done in two ways: using the d( function or using the F3 menu. In this article, we will explain both methods with examples.
Using the d( function
The d( function is a built-in function on the ti-89 calculator that can find the value or the expression of a derivative. For example, suppose we want to find the derivative of the function f(x) = x^2 + 3x – 5f(x)=x2+3x−5 at the point x = 2x=2.
To find the derivative using the d( function, follow these steps:
- Press the
ONbutton to turn on the calculator. - Press the
MODEbutton and make sure thatEXACTis selected for the exact/approximate mode. - Press the
HOMEbutton to go to the home screen. - Press the
2NDbutton and then press theMATHbutton to access the math menu. - Scroll down until you see the
d(function and pressENTERto select it. - Enter the function, the variable, and the point of evaluation separated by commas. For our example, we would enter
X^2+3X-5,X,2. - Press the
)button to close the parentheses and pressENTERto calculate the derivative.
The calculator will display the derivative as 7. This means that the slope of the function f(x)f(x) at the point x = 2x=2 is 77.
Using the F3 menu
The F3 menu is a shortcut menu on the ti-89 calculator that can perform various calculus operations, such as finding derivatives, limits, integrals, and sums. For example, suppose we want to find the derivative of the function g(x) = \sin(x) + \cos(x)g(x)=sin(x)+cos(x).
To find the derivative using the F3 menu, follow these steps:
- Press the
ONbutton to turn on the calculator. - Press the
MODEbutton and make sure thatEXACTis selected for the exact/approximate mode. - Press the
HOMEbutton to go to the home screen. - Enter the function that you want to differentiate. For our example, we would enter
sin(X)+cos(X). - Press the
F3button to access the calculus menu. - Scroll down until you see the
1:Derivativeoption and pressENTERto select it. - Enter the variable of differentiation. For our example, we would enter
X. - Press the
ENTERbutton to calculate the derivative.
The calculator will display the derivative as cos(X)-sin(X). This means that the expression of the derivative of the function g(x) is cos(x) – sin(x)cos(x)−sin(x).
Summary
In this article, we learned how to find derivatives on a ti-89 calculator using two methods: using the d( function and using the F3 menu. Derivatives are useful for analyzing the behavior of functions, such as finding the maximum or minimum values, the increasing or decreasing intervals, and the concavity. We hope this article was helpful and informative. For more information on derivatives and other calculus concepts, you can check out this website.