Class 4 Recap (Mon Sept 11)

Class Info

• Date: Mon, Sept 11
• Meeting Info: 12p-1:40p, N700

Topics

• Introduced “delta y over delta x” notation for slope of the secant line:
• Examples from WebWork “Derivatives – Limit Definition”:
  • Went through guiding text in WebWork exercises:
  • Note: what in this WebWork set is called “instantaneous slope” is also called the “instantaneous rate of change” and is “the slope of the tangent line at x=a”
    • this is what we will call the derivative of f at x = a, for which we will use the notation f'(a)
  • Revisited this figure and discussed in context of new notation:
  • Went through Derivatives – Limit Definition: Problem 1:
  • 
  • We went one step further and found the equation of the tangent line to f(x) at that point – using the point-slope form (since we were given the point and calculated the slope!)
  • See the Desmos graph illustrating this example here: https://www.desmos.com/calculator/kfllhpu38j
  • Derivatives – Limit Definition: Problem 2:
  • 

To-Do After Class

• Work through “Derivatives – Limit Definition” (due Monday, Sept 18)
• Read OpenStax Sec 3.1: Defining the Derivative