First and Second Derivative of Parametric Equations – Concavity

This video provides an example of how to determine the first and second derivative of a curve given by parametric equations. It also explains how to determine the intervals of t for which the curve is concave up or concave down.

Determine the Points Where the Tangent Lines are Horizontal or Vertical Using Parametric Equations

This video explains how to determine the points on a parametric curve where the tangent lines are horizontal or vertical.

Determine the First and Second Derivative Given Parametric Equations

This video provides an example of how to determine the first derivative and second derivative at a given value of t. Then determine the slope of the tangent line and the concavity.

Ex 3: Equation of a Tangent Line to a Curve Given by Parametric Equations

This video provides an example of how to determine the equation of a tangent line when the curve is given by parametric equations.

Ex 2: Equation of a Tangent Line to a Curve Given by Parametric Equations

This video provides an example of how to find the derivative of parametric equations and find the equation of the tangent line at a given value of t.

Ex 1: Equation of a Tangent Line to a Curve Given by Parametric Equations

This video provides an example of how to find the derivative of parametric equations and find the equation of the tangent line at a given value of t.

Ex: Critical Numbers / Relative Extrema / Second Derivative Test

This video provides an example of how to find relative extrema using the second derivative test.

Ex: Critical Numbers / Relative Extrema / First Derivative Test

This video provides an example of how to find relative extrema using the first derivative test.

Ex 1: First and Second Derivatives Using the Chain Rule – f(x)=tan(2x)

This video explains how to find the first and second derivatives and derivative function values.  The results are verified graphically.

Ex 2: First and Second Derivatives Using the Chain Rule – f(x)=ln(cos(x))

This video explains how to find the first and second derivatives and derivative function values.  The results are verified graphically.