Class Info

  • Date: Mon, Sept 18
  • Meeting Info: 12p-1:40p, N700

Announcement

We will have our first quiz at the end of class on Wednesday. It will consist of an exercise similar to the exercises in “Derivatives – Limit Definition”, i.e, calculating the derivative of a given function at a given point using the limit definition of the derivative.

You don’t need to memorize the limit definition–it will be provided.

Topics

Went through an example from “Derivatives – Functions”, continuation of the example we started at the end of Class 5–finding the derivative f'(x) for f(x) = 5/x:

We used f'(x) to find the slope and then the equation of the tangent line at x = 7 (using the point-slope form):

We went one step further and wrote down the equation of the tangent line for this function at an arbitrary point (a, f(a)):

We also solved the x-values where the slope of the tangent line is 1.

See this Desmos graph, which shows y = 5/x together with the tangent line at (a, f(a)) for various values of x = a.

We similarly calculated the derivative of f(x) = x^2:

Next time we will generalize this to find “the Power Rule”–the derivative of any power function f(x) = x^n (See Sec 3.3 – Differentiation Rules)

To-Do After Class

  • Work on “Derivatives – Functions” (due Thurs Sept 21)