
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