Implicit Differentiation with TI-89 Calculator

This tutorial demonstrates how to perform implicit differentiation using the TI-89 graphing calculator. It guides users through accessing the implicit differentiation function in the calculus menu and provides step-by-step instructions for solving two example equations: a circle equation and a cubic equation. The tutorial emphasizes the importance of correctly entering variables and highlights the default settings for derivative order.

What is the first step to access the implicit differentiation function on the TI-89 calculator?

• Press F3

• Press F1

• Press F4

• Press F2

Where is the implicit differentiation function located in the TI-89 calculator?

• Under the calculus menu

• Under the matrix menu

• Under the graph menu

• Under the algebra menu

What is the default order of differentiation if not specified?

• Fourth derivative

• First derivative

• Third derivative

• Second derivative

In the first example, what is the equation used for implicit differentiation?

• x^2 + y^2 = 25

• x^3 + y^3 = 27

• x^3 - y^3 = 9

• x^2 - y^2 = 16

What is the result of dy/dx for the equation x^2 + y^2 = 25?

• Negative x divided by y

• y divided by x

• x divided by y

• Negative y divided by x

In the second example, how should 'xy' be entered in the equation?

• As x divided by y

• As x times y

• As x minus y

• As x plus y

What is the equation used in the second example for implicit differentiation?

• x^2 - y^2 + 4xy = 0

• x^3 - y^3 + 9xy = 0

• x^2 + y^2 - 4xy = 0

• x^3 + y^3 - 9xy = 0

What is the independent variable in the second example?

• y

• z

• x

• w

What is the result of dy/dx for the equation x^3 + y^3 - 9xy = 0?

• 3x - y^2 divided by x^2 - 3y

• x^2 - 3y divided by 3x - y^2

• 3x + y^2 divided by x^2 + 3y

• x^2 + 3y divided by 3x + y^2

What is the dependent variable in the second example?

• w

• x

• y

• z