Tangent Line Equations and Derivatives

This video tutorial explains how to find the equation of a tangent line to a curve at a given point. It covers the process of calculating the Y value and slope, deriving the tangent line equation using point-slope form, and solving example problems. The tutorial also addresses solving cubic equations in the context of tangent line problems, providing multiple methods for finding solutions.

What are the three components needed to find the equation of a tangent line?

• The value of x, the value of y, and the slope

• The value of y, the value of z, and the slope

• The value of x, the value of y, and the intercept

• The value of x, the value of z, and the slope

How do you find the y-value for the tangent line equation?

• By solving for x in the derivative equation

• By using the slope-intercept form

• By plugging the x-value into the original equation

• By differentiating the original equation

What is the first step in finding the slope of the tangent line?

• Use the point-slope form

• Solve for y in the original equation

• Differentiate the original equation

• Plug the x-value into the original equation

Which form is used to initially write the equation of the tangent line?

• Point-slope form

• Quadratic form

• Standard form

• Slope-intercept form

How do you convert the tangent line equation from point-slope to slope-intercept form?

• By multiplying the x-value by the slope

• By subtracting the y-value from both sides

• By distributing the slope and simplifying

• By adding the slope to both sides

In the example problem, what is the x-value used to find the tangent line equation?

• x = 3

• x = 2

• x = 1

• x = 4

What is the slope of the tangent line in the example problem with x = 2?

• 3

• 4

• 5

• 6

What method is suggested for solving a cubic equation when finding the y-value?

• Using a graphing calculator

• Using the quadratic formula

• Using substitution

• Using elimination

What is the derivative of y^3 with respect to y?

• 3y^2

• 3y

• y^2

• y

What is the final slope of the tangent line in the advanced example?

• -8/15

• 15/8

• 8/15

• -15/8