Mathematics 133 -- Intensive Calculus

Quiz 6 -- Things to Know

November 1, 2000

The sixth graded quiz of the semester will be given in class on Friday, November 3. There will be three or four questions similar to problems from the latest problem set. One will be a "word problem" where you will need to use information about rates of change or concavity to analyze some situation. You should know the following material from sections 4,5,6 of Chapter 4 in the text:

1. The Chain Rule for derivatives: d/dx(f(g(x))) = f '(g(x)) g '(x)
2. Derivatives of the trigonometric functions:
   • d/dx(sin(x)) = cos(x),
   • d/dx(cos(x)) = -sin(x)
3. Derivatives of inverse functions of known functions:
   • d/dx(ln(x)) = 1/x
   • d/dx(arcsin(x) = 1/sqrt(1 - x²)
   • d/dx(arctan(x) = 1/(1 + x²)

Be able to use these in combination with the sum, product, and quotient rules.

Good Review Problems:

1. Section 4.4/problems like 1 - 30, 40, 43, 44
2. Section 4.5/problems like 1 - 29, 31, 33, 35
3. Section 4.6/problems like 1 - 25, 27, 29