Mathematics 133 -- Intensive Calculus

Quiz 5 -- Things to Know

October 18, 2000

The fifth graded quiz of the semester will be given in class on Friday, October 20. There will be three or four questions similar to problems from the fifth problem set. You should know the following material.

1. The Meanings of the First and Second Derivatives of f(x) (Section 2.5): Know how the sign of f ' (x) is related to whether the function is increasing or decreasing at x, and how the sign of f '' (x) is related to concavity. Know how to sketch the graph y = f '' (x) qualitatively, given the graph y = f(x) or y = f ' (x).
2. Derivative Formulas (Sections 1,2,3 from Chapter 4)
   1. f'(x) = n x^n-1 for the power function f(x) = xⁿ
   2. f'(x) = ln(a) a^x for the exponential function f(x) = a^x
   3. Sum and constant multiple rules
   4. Product rule -- d/dx(f(x)g(x)) = f(x)g ' (x) + g(x)f ' (x)
   5. Quotient rule -- d/dx(f(x)/g(x)) = (g(x)f ' (x) - f(x)g ' (x))/(g(x))²

Good Review Problems:

1. Section 2.5/problems like 1 - 6, 15 (also practice sketching the graphs of y = f ' (x) and y = f '' (x) if the graph of y = f(x) is the given one in figure 2.39),16,17
2. Section 4.1/problems like 1 - 20
3. Section 4.2/problems like 1 - 21
4. Section 4.3/problems like 1 - 23