Mathematics 133 -- Intensive Calculus for Science 1

Quiz 6

October 24, 2001

The sixth regular quiz of the semester will be given in class on Friday, October 26. It will cover the material from sections 3.1 and 3.2 from this week's problem set. You may use a calculator on this quiz. The specific topics to be covered will be:

• First ``shortcut rules'' for computing derivatives:
  1. The derivative power rule: d/dx(xⁿ) = n x^n-1.
  2. The derivative sum rule: d/dx(f(x) + g(x)) = f'(x) + g'(x)
  3. The derivative constant multiple rule: d/dx(cf(x)) = cf'(x)
  4. The derivative exponential rule: d/dx(a^x) = a^x ln(a)
  Know how to use these singly and in combination. Also be able to do some preliminary algebra to put functions into a form where these methods apply, if necessary -- for instance splitting up quotients into sums of constants times powers, or multiplying out factored expressions.
• Applications of these rules to rate of change problems, questions about whether a function is increasing or decreasing, concave up or concave down.

Good Review Problems

• Problems like 3.1/1-31, 45, 55, 60
• Problems like 3.2/1-26, 37, 39