Math 180 A
Spring 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 Friday, April 9, and
will cover section 3.5 through section 4.4 of the textbook. In particular, be prepared
to:
- 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 do define the basic hyperbolic functions (sinh, cosh, tanh) and
take derivatives of them.
- 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.
- Be able to state the corollaries to the mean value theorem and apply
them to simple problems (including graphing and to differential equations (problems 27 -
35 on page 252 would be
a good review for this part)).
- Be able to discover (using first and second derivatives) where a
function is
- increasing or decreasing
- concave up or down
- has a maximum or minimum
- has a point of inflection
Any questions? Please ask!