Test 2 Topics

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You should be able to:

  • Determine whether the limit exists by looking at the graph of . Sec 1.4 
  • Draw the graph of a function in which the limit  does not exist. Sec 1.4 (also, see Test 2 practice problems)
  • Determine whether a function is differentiable at a point by looking at the graph for . Sec 1.5
    • Recall that is differentiable at a point when the following limit exists: exists.
  • Determine whether a function is continuous at a point.
    • Recall that is continuous at a point when the limit exists is equal to the value . Sec 1.5
  • Interpret the derivative of at a point as the (instantaneous) rate of change of . Sec 1.8
    • In populations applications: we call the derivative the growth rate
    • In physical applications: we call the derivative velocity
  • Compute the average rate of change, and compare it to the derivative at a point. Sec 1.8
  • Interpret the second derivative of at a point as the (instantaneous) rate of change of the rate of change of . Sec 1.8
    • In population application: we can the second derivative the rate of change of the growth rate
    • In physical applications: we call the second derivative acceleration
  • Compute the second derivative Sec 1.6-1.7
    • I will specifically test you on using the general power rule. Sec 1.6
  • Given a function compute its intervals of increasing and decreasing Sec 2.2
  • Given a function compute its relative minima and maxima Sec 2.3
  • Given a function compute its intervals of concavity Sec 2.2
  • Given a function compute its inflection points Sec 2.3
  • Use the above information to sketch the graph of  Sec 2.2-2.4
    • You will not be asked to find the and intercepts for .
  • Given information about , , and , at a point sketch the graph of near the point . Sec 2.2
  • Interpret intervals of increasing and decreasing, relative maxima and minima, and concavity in applications (focus on physical applications) See Application of derivative HW and examples from lecture
  • Given information about and (in a graphical form) answer questions about . Sec 2.2 
    • Specifically try numbers 23, 24, 43, and 44 from Sec 2.2; note that number 44 is the test review problem number 4

Good luck!