Mathematics 133 -- Intensive Calculus for Science 1

Quiz 6

October 18, 2005

The sixth regular quiz of the semester will be given in class on Friday, October 21. It will cover the material from sections 2.5,2.6, and 3.1 and 3.2. You may use a calculator on this quiz. The specific topics to be covered will be:

• The second derivative f'' = (f')' and its connection with the concavity of the graph y = f(x):
  1. If f'' > 0 on an interval, then y = f(x) is concave up on that interval
  2. If f'' < 0 on an interval, then y = f(x) is concave down on that interval
• Differentiability, and what behavior causes a function not to be differentiable at some x (discontinuities, sharp corners, vertical tangents)
• 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)
  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.

Good Review Problems

• Problems like 2.5/1-12
• Problems like 3.1/1-31