Math 180 D
Fall 2010
Exam 3 Review
Disclaimer: I have attempted to be comprehensive in the
following, but important items may have been omitted by mistake. If
you see such an omission, please let me know, but you are responsible
for all of the lecture material to date.
The third hour exam for Math 180 will be held on Tuesday, November 16, and
will cover section 3.3 through section 4.2 of the textbook. In particular, be prepared
to:
- Be able to discuss the derivative as a rate of change. Be able to
calculate velocity, acceleration, and jerk.
- Be able to use the chain rule.
- Be able to work with inverse trigonometric functions.
- Be able to take the derivatives of inverse trigonometric functions.
- Be able to calculate tangent and normal lines (again), including their
application to implicit differentiation.
- Be able to give linear approximations to functions and to estimate
values.
- Be able to solve rate of change problems, including "word problems".
- Use implicit differentiation, including (but not limited to), the
calculation of functions implicitly defined by an equation, the calculation
of inverse functions (including the inverse trigonometric functions), and
the use of logarithmic differentiation.
- Be able to state (with preconditions), explain, and apply the Extreme
Value Theorem.
- Be able to state (with preconditions, explain, and apply Rolle's Theorem
and the Mean Value Theorem. Statements of all theorems must be precise
and include the requirements (preconditions) for the theorem to be true.
Any questions? Please ask!