Understanding Tangent Lines in Parametric Curves

This video tutorial explains how to find points on a parametric curve where horizontal or vertical tangent lines occur. It covers the concept of slope being zero for horizontal tangents and undefined for vertical tangents. The tutorial provides examples using different types of functions, including linear, quadratic, cubic, and trigonometric functions, to demonstrate the process of finding these tangent points.

What is the condition for a parametric curve to have a horizontal tangent line?

• The curve is a circle.

• The slope is undefined.

• The slope is equal to zero.

• The curve is a straight line.

In Example 1, what is the value of t where the horizontal tangent line occurs?

• t = 3

• t = 1

• t = 0

• t = 2

For the parametric function in Example 1, what is the x-coordinate of the point where the horizontal tangent line occurs?

• x = 14

• x = 11

• x = 8

• x = 5

In Example 2, what is the t value for which a vertical tangent line occurs?

• t = 3

• t = 2

• t = 0

• t = -1

What is the y-coordinate of the point where the vertical tangent line occurs in Example 2?

• y = 9

• y = 12

• y = 18

• y = 15

In Example 3, what is the derivative of y with respect to θ?

• 4cos(θ)

• 3sin(θ)

• 4sin(θ)

• 3cos(θ)

For the trigonometric function in Example 3, at which angle does a horizontal tangent line occur?

• θ = 0

• θ = π/2

• θ = π

• θ = 2π

What is the x-coordinate of the point where the vertical tangent line occurs when θ = 0 in Example 3?

• x = 0

• x = 2

• x = 4

• x = 6

In Example 3, what is the y-coordinate of the point where the horizontal tangent line occurs at θ = 3π/2?

• y = 1

• y = 0

• y = 2

• y = -1

What is the general method to find vertical tangents in parametric functions?

• Set the denominator of dy/dx to zero.

• Set the numerator of dy/dx to zero.

• Set both numerator and denominator of dy/dx to zero.

• Set the original function to zero.