Mathematics 133 -- Intensive Calculus for Science 1

Quiz 5

October 17, 2001

This week, we are back to our regular five-day schedule. The fifth regular quiz of the semester will be given in class on Friday, October 19. It will cover the material from sections 2.4, 2.5, and 2.6 from this week's problem set. You may use a calculator on this quiz (but I'd be surprised if you found you needed one!). The specific topics to be covered will be:

• The derivative function f'(x) for a function f(x). Know:
  1. How to spot points on a graph where f'(x) = 0, where f'(x) > 0 (intervals where the function f is increasing), and where f'(x) < 0 (intervals where f is decreasing).
  2. How to compute a simple example (say a degree 2 polynomial function, or f(x) = 1/x, etc.) from the limit definition of f'. (See section 2.4 problems 13-16)
  3. How to sketch y = f'(x), given the graph y = f(x) (See section 2.4/23 - 30)
• The derivative as rate of change, the units of dy/dx, interpreting statements about dy/dx (like Section 2.5/1-4,11-14)
• The second derivative f''(x), its relation to concavity Know
  1. How to identify where f''(x) > 0 (intervals where the graph y = f(x) is concave up, or f'(x) is increasing), and where f''(x) < 0 (intervals where y = f(x) is concave down, or f'(x) is decreasing). (See Section 2.6/1-4.)
  2. The interpretation of the second derivative as acceleration.