Fall 2010 
MA 22000 – Topics List 

I. Evaluating a function when the input is not numeric 
• For example: (f(x+Δx)−f(x)) /Δx  
 
II. Composition of functions 
 
III. Finding limits 
• Using a table 
• From a graph 
• By direct substitution 
• By factoring and canceling 
• In the definition of derivative (limit of a difference quotient) 
 
IV. Finding values where function is not differentiable 
• Using a graph 
 
V. Using derivative rules 
• Power rule 
• Product rule 
• Quotient rule 
• General power rule (chain rule) 
 
VI. Applications using the derivative 
• Finding the slope/equation of a tangent line; finding point(s) where slope of a tangent line 
has a given value 
• Finding the rate of change of a function 
• Finding a marginal function and its use in estimating actual change 
• Finding velocity 
• Finding the value of a derivative at a given point 
 
VII. Applications not using the derivative 
• Finding the y-value of a point 
• Finding the average rate of change  
• Finding the actual change  
• Estimating the slope of a graph at a point using a grid 
• Estimating the average rate of change and rate of change of a function using a grid 
 
VIII
• Lines in the plane and slope