Implicit Differentiation with TI-89 Calculator

This tutorial demonstrates how to evaluate the derivative of an implicit equation using the TI-89 graphing calculator. It covers the process of using the implicit differentiation function from the calculus menu to find the slope of the tangent line at a given point. Two examples are provided: one involving a circle equation and another with mixed terms. The tutorial guides users through entering equations, selecting variables, and evaluating derivatives at specific points.

What is the main objective of this tutorial?

• To learn how to graph equations on the TI-89 calculator.

• To determine the slope of a tangent line using implicit differentiation.

• To solve linear equations using the TI-89 calculator.

• To find the area under a curve using the TI-89 calculator.

Which menu on the TI-89 calculator contains the implicit differentiation function?

• Graph menu

• Calculus menu

• Statistics menu

• Algebra menu

What is the default order of the derivative when using the implicit differentiation function?

• Third derivative

• Fourth derivative

• First derivative

• Second derivative

In the first example, what is the equation entered into the calculator?

• x^2 + y^2 = 10

• x^2 - y^2 = 25

• x^2 + y^2 = 25

• x^2 - y^2 = 10

What is the slope of the tangent line at the point (-3, 4) in the first example?

• 1

• -34

• 34

• 0

What is the next step after entering the equation in the implicit differentiation function?

• Calculate the integral

• Solve for x

• Press the graph button

• Enter the independent and dependent variables

In the second example, what additional term is included in the equation?

• x^3

• y^2

• x * y

• x^2

What is the slope of the tangent line at the point (1, 1) in the second example?

• 2

• -1

• 0

• 1

How do you evaluate the derivative at a specific point using the calculator?

• By entering the point directly into the equation

• By using the graphing function

• By using the vertical bar and entering the point

• By solving the equation manually

What is the purpose of using the catalog in the TI-89 calculator during this process?

• To graph the equation

• To solve the equation

• To find the derivative

• To access the 'and' function