Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Higher Order Derivatives
Language:
English
Media Formats:
eBook, Interactive

# Higher order derivatives and graphs modules

## Overview

After completing this section, students should be able to do the following.

• Use the first derivative to determine whether a function is increasing or decreasing.
• Define higher order derivatives.
• Compare differing notations for higher order derivatives.
• Identify the relationships between the function and its first and second derivatives.
• Sketch a graph of the second derivative, given the original function.
• Sketch a graph of the original function, given the graph of its first or second derivative.
• Sketch a graph of a function satisfying certain constraints on its higher-order derivatives.
• State the relationship between concavity and the second derivative.
• Interpret the second derivative of a position function as acceleration.
• Calculate higher order derivatives.
• Given the graph of a position function, find time intervals where the velocity is positive/negative
• Given the graph of a position function, find time intervals where the velocity is increasing/decreasing

# Rates of rates

## Ximera Module

Two young mathematicians look at graph of a function, its first derivative, and its second derivative.

# Higher order derivatives and graphs

## Ximera Module

Here we make a connection between a graph of a function and its derivative and higher order derivatives.

# Concavity

## Ximera Module

Here we examine what the second derivative tells us about the geometry of functions.

# Poison, velocity, and acceleration

## Ximera Module

Here we discuss how position, velocity, and acceleration relate to higher derivatives.