TI-89 Graphing Calculator: Tangent Line Equations

This tutorial demonstrates how to determine the equation of a tangent line using the TI-89 graphing calculator. It covers two examples: the first involves a quadratic function, and the second involves a trigonometric function. The tutorial guides users through entering functions, setting the calculator to the correct mode, and using the calculator's features to find tangent lines. It also explains how to interpret the results, including understanding decimal approximations.

What is the primary task discussed in this tutorial?

• Calculating integrals

• Graphing linear functions

• Finding the equation of a tangent line

• Solving quadratic equations

Which function is used in the first example to find the tangent line?

• H(x) = x^3 + 2

• G(x) = sin(x)

• F(x) = 14x^2 - 4

• J(x) = e^x

What is the slope of the tangent line found in the first example?

• 0

• 1

• 3

• 2

Before finding the tangent line for a trigonometric function, what mode should the calculator be in?

• Degree mode

• Radian mode

• Scientific mode

• Graphing mode

What is the trigonometric function used in the second example?

• sec(x)

• 2sin(2x)

• tan(x)

• cos(x)

What adjustment is made to the graph window to better view the function?

• Change X scale to 1

• Change Y scale to 2

• Change X Min to -3 and X Max to 3

• Change Y Min to -10 and Y Max to 10

What is the purpose of adjusting the graph window in the second example?

• To zoom out for a wider view

• To switch to 3D graphing

• To focus on the point of tangency

• To change the function's color

What is the slope of the tangent line in the second example?

• 1

• 2

• 4

• 3

Why does the calculator provide a decimal approximation for the tangent line equation?

• The function is too complex

• The calculator is in approximate mode

• The exact value is not possible

• The function is not continuous

How can the exact value of the tangent line's vertical intercept be verified?

• By using the calculator's exact mode

• By switching to degree mode

• By using a different calculator

• By graphing a different function