AP Calculus AB: Unit 1 Section 1

Average Rate of Change

  • Finding AROC from a function over a specific interval
    1. find the related points
    2. determine slope between the two points
    3. the slope between the two points is the average rate of change from the given domain values from given intervals

Slope of a Secant Line

Finding slope of the secant line from a function over a specific interval
  1. find the related points
  2. determine slope between the two points
  3. the slope between the two points is the slope of the secant line

Instantaneous Rate of Change

Finding IROC of the tangent line from a function over at a specific given point point
  1. find the related point
  2. determine the limit of the function at the specific x coordinate of the given point
  3. OR determine the value of the derivative function at the specific x coordinate of the given point
This method of determining IROC has limitations 
  • can only be used for a particular value of a
  • It does help to be able to factor polynomials with this method
  • It does help to able to perform synthetic division of polynomials with this method
Both of these methods require tedious algebraic manipulation to complete.
  • It does help to be able to rewrite algebraic expressions with these methods 
  • These methods should be useful for all domain values of x not just one particular example
  • When algebra is done properly denominators h and delta x should be able to be canceled out

Slope of the Tangent Line

Finding slope of the tangent line from a function over at a specific given point point
  1. find the related point
  2. determine the limit of the function at the specific x coordinate of the given point
  3. OR determine the value of the derivative function at the specific x coordinate of the given point

Practice

These worksheets allows practice with 
AROC and Equations of Secants
Links and Resources
​Mr Hickman's Resources