MATH 160 004 - Review Suggestions for Test #2 -- 10/23/07

This is the final form of this list.

Be sure to show your work on the test. On the first page of the test it says

Support your problem solutions with written solution steps. Unsupported correct answers won't get as many points as correct answers supported by solution steps. Unsupported incorrect answers will miss out on any partial credit that's available.

1. Don't worry about story problems this time -- we'll save them for Test #3.
2. Calculator policy: You can bring along a TI-30, or equivalent. I'm allowing myself the power to declare calculators "too able", and thus not useable on the exam:
   • No text-storage capability
   • No graphing capability
   • No computer-algebra capability
   • No communication capability (No IR, No bluetooth, ...)
3. The test will cover the material of assignments #13 - the first #21. roughly. That is, sections 3-5, 3-6, 3-7, 4-1, 4-2, 4-3, 4-4, 5-1, 5-2, 5-3.
4. MATH-143 Things:
   • Writing correct difference quotients: click here for problems.
   • Factoring
   • Least Common Denominator (a perennial)
   • Recognizing and solving a quadratic equation
   • Laws of Exponents
   • Laws of Logarithms
   • The graphs of y=e^x, y=e^3x, and y=e^-2x.
   • The graph of y = ln(x).
5. The new short-cut derivative-finding methods so far:
   • the derivative of the natural-logarithm function
   • the derivative of e^x
   • the Product Rule (and remembering to use it)
   • the Quotient Rule (and remembering to use it)
   • the Chain Rule

     The Chain Rule and its special cases:

     • If y = f(g(x)), then y' =
     • If y = (g(x))ⁿ, then y' =
     • If y = e^g(x), then y' =
     • If y = ln(g(x)), then y' =

     Don't forget the moo!

6. You'll still have to find tangent-line equations (see for instance, 4-2: 15-26, 4-3: 49-54, 4-4: 63-68).
7. You do need to be conversant with the "intuitive content" of the tangent line idea. See, for instance, problem 2 on this alternative quiz.
8. The idea of dy is a repackaging of the idea that the line tangent to f at x = A is close to the graph of f for values of x close to A.
9. Chapter 5, so far, has been taken up with how the derivatives g' and g'' indicate the salient features of the graph of g.
   • critical values - what is the graph of g doing at a critical value. Does the absolute-value function have critical values?
   • local extremes
   • inflection points
   • intervals on which the function in question is increasing and intervals on which it is decreasing.
   • intervals on which the the derivative of the function in question is increasing and intervals on which it is decreasing.
   • concavity
   • How a g' sign-change chart arises from factored g'(x) and what it tells about the graph of g.
   • How an h'' sign-change chart arises from factored h''(x) and what it tells about the graph of h.
10. L'Hôpital's Rule - in the first #21 there were some problems requiring us to do more than one l'Hˆpitalian transformation.
11. All of the problems except for problem 2 (story problem) on the Valentine's-Day Test #1 from 2003 (in the Old-Tests collection) are relevant to us. This old test does not involve e^x and the natural logarithm. Note that problem 2 is a MATH-143 problem which is solvable by parabola knowhow.
12. The spring-2003 Test #2 has e^x problems. Ignore problem 6, the story problem.
13. All of the spring-1999 Test #2's problems are relevant, except for the story problem at the end.